2 the logical function f is given by the expression x. The logical function F is given by the expression
Based on: demo versions of the Unified State Exam in computer science for 2015, on the textbook by Lyudmila Leonidovna Bosova
In the previous part 1, we discussed with you the logical operations Disjunction and Conjunction, all that remains for us is to analyze inversion and move on to solving the Unified State Exam task.
Inversion
Inversion- a logical operation that associates each statement with a new statement, the meaning of which is opposite to the original one.
The following characters are used to write inversion: NOT, `¯`, ` ¬ `
The inversion is determined by the following truth table:
Inversion is otherwise called logical negation.
Any complex statement can be written in the form logical expression— expressions containing logical variables, logical operator signs and parentheses. Logical operations in a logical expression are performed in the following order: inversion, conjunction, disjunction. You can change the order of operations using parentheses.
Logical operations have the following priority: inversion, conjunction, disjunction.
And so, before us is task No. 2 from the Unified State Exam in computer science 2015
Alexandra was filling out the truth table for the expression F. She only managed to fill out a small fragment of the table:
x1 x2 x3 x4 x5 x6 x7 x8 F 0 1 0 1 0 1 1 1 1 What expression can F be?
What makes solving the problem much easier is that in each version of the complex expression F there is only one logical operation: multiplication or addition. In case of multiplication /\ if at least one variable is equal to zero, then the value of the entire expression F must also be equal to zero. And in the case of addition V, if at least one variable is equal to one, then the value of the entire expression F must be equal to 1.
The data that is in the table for each of the 8 variables of the expression F is quite enough for us to solve.
Let's check expression number 1:
- ? /\ 1 /\ ? /\ ? /\ ? /\ ? /\ ? /\ 0 )
- from the second line of the table x1=1, x4=0 we see that F is possible and can be equal to = 1 if all other variables are equal to 1 (1 /\ ? /\ ? /\ 1 /\ ? /\ ? /\ ? /\ ? )
- according to the third line of the table x4=1, x8=1 we see that F=0 (? /\ ? /\ ? /\ 0 /\ ? /\ ? /\ ? /\ 0 ), and in the table we have F=1, and this means that expression number one is for us DEFINITELY NOT SUITABLE.
Let's check expression number 2:
- from the first line of the table x2=0, x8=1 we see that F is possible and can be equal to = 0 if all other variables are equal to 0 (? V 0 V ? V ? V ? V ? V ? V 0 )
- from the second line of the table x1=1, x4=0 we see that F = 1 ( 1 V ? V ? V 1 V ? V ? V ? V ? )
- according to the third line of the table x4=1, x8=1 we see that F is possible and can be equal to = 1 if at least one of the remaining variables is equal to 1 ( ?
V ?
V ?
V 0
V ?
V ?
V ?
V 0
)
Let's check expression number 3:
- from the first line of the table x2=0, x8=1 we see that F=0 (? /\ 0 /\ ? /\ ? /\ ? /\ ? /\ ? /\ 1 )
- from the second line of the table x1=1, x4=0 we see that F =0 (0 /\ ? /\ ? /\ 0 /\ ? /\ ? /\ ? /\ ? ), and in the table we have F=1, and this means that expression number three gives us DEFINITELY NOT SUITABLE.
Let's check expression number 4:
- from the first line of the table x2=0, x8=1 we see that F=1 ( ? V 1 V ? V ? V ? V ? V ? V 0 ), and in the table we have F=0, and this means that expression number four gives us DEFINITELY NOT SUITABLE.
When solving a task on the unified state exam, you need to do exactly the same thing: discard those options that are definitely not suitable based on the data in the table. The remaining possible option (as in our case, option number 2) will be the correct answer.
Catalog of tasks.
Number of programs with a mandatory stage
Take tests on these tasks
Return to task catalog
Version for printing and copying in MS Word
Performer A16 converts the number written on the screen.
The performer has three teams, which are assigned numbers:
1. Add 1
2. Add 2
3. Multiply by 2
The first of them increases the number on the screen by 1, the second increases it by 2, the third multiplies it by 2.
A program for performer A16 is a sequence of commands.
How many programs are there that convert the original number 3 into the number 12 and at the same time the program's calculation trajectory contains the number 10?
A program's computation trajectory is a sequence of results from the execution of all program commands. For example, for program 132 with the initial number 7, the trajectory will consist of the numbers 8, 16, 18.
Solution.
The required number of programs is equal to the product of the number of programs that obtain the number 10 from the number 3 by the number of programs that obtain the number 12 from the number 10.
Let R(n) be the number of programs that convert the number 3 into the number n, and P(n) be the number of programs that convert the number 10 into the number n.
For all n > 5 the following relations are true:
1. If n is not divisible by 2, then R(n) = R(n - 1) + R(n - 2), since there are two ways to obtain n - by adding one or adding two. Similarly P(n) = P(n - 1) + P(n - 2)
2. If n is divisible by 2, then R(n) = R(n - 1) + R(n - 2) + R(n / 2). Similarly P(n) = P(n - 1) + P(n - 2) + P(n / 2)
Let us sequentially calculate the values of R(n):
R(5) = R(4) + R(3) = 1 + 1 = 2
R(6) = R(5) + R(4) + R(3) = 2 + 1 + 1 = 4
R(7) = R(6) + R(5) = 4 + 2 = 6
R(8) = R(7) + R(6) + R(4) = 6 + 4 + 1 = 11
R(9) = R(8) + R(7) = 11 + 6 = 17
R(10) = R(9) + R(8) + R(5) = 17 + 11 + 2 = 30
Now let's calculate the values of P(n):
P(11) = P(10) = 1
P(12) = P(11) + P(10) = 2
Thus, the number of programs that satisfy the conditions of the problem is 30 · 2 = 60.
Answer: 60.
Answer: 60
Source: Demo version of the Unified State Exam 2017 in computer science.
1. Add 1
2. Add 3
How many programs are there for which, given the initial number 1, the result is the number 17 and at the same time the computation trajectory contains the number 9? A program's computation trajectory is a sequence of results from the execution of all program commands. For example, for program 121 with the initial number 7, the trajectory will consist of the numbers 8, 11, 12.
Solution.
We use the dynamic programming method. let's create an array dp, where dp[i] is the number of ways to get the number i using such commands.
Dynamics base:
Transition formula:
dp[i]=dp + dp
This does not take into account the values for numbers greater than 9, which can be obtained from numbers less than 9 (thus skipping the trajectory of 9):
Answer: 169.
Answer: 169
Source: Training work in COMPUTER SCIENCE, grade 11 November 29, 2016 Option IN10203
Performer May17 converts the number on the screen.
The performer has two teams, which are assigned numbers:
1. Add 1
2. Add 3
The first command increases the number on the screen by 1, the second increases it by 3. The program for the May17 performer is a sequence of commands.
How many programs are there for which, given the initial number 1, the result is the number 15 and at the same time the computation trajectory contains the number 8? A program's computation trajectory is a sequence of results from the execution of all program commands. For example, for program 121 with the initial number 7, the trajectory will consist of the numbers 8, 11, 12.
Solution.
We use the dynamic programming method. Let's create an array dp, where dp[i] is the number of ways to get the number i using such commands.
Dynamics base:
Transition formula:
dp[i]=dp + dp
But this does not take into account numbers that are greater than 8, but we can get to them from a value less than 8. The following will show the values in cells dp from 1 to 15: 1 1 1 2 3 4 6 9 9 9 18 27 36 54 81 .
Job source: Solution 2437. Unified State Exam 2017. Computer Science. V.R. Leschiner. 10 options.
Task 2. The logical function F is given by the expression . Determine which column of the truth table of the function F corresponds to each of the variables x, y, z.
In your answer, write the letters x, y, z in the order in which their corresponding columns appear (first - the letter corresponding to the 1st column, then - the letter corresponding to the 2nd column, then - the letter corresponding to the 3rd column) . Write the letters in the answer in a row; there is no need to put any separators between the letters.
Solution.
Let us rewrite the expression for F taking into account the priorities of the operations of negation, conjunction and disjunction:
.
Consider the 4th row of the table (1,1,0)=0. From this we can see that the third place must be either the variable y or the variable z, otherwise the second bracket will contain 1, which will lead to the value F=1. Now consider the 5th row of the table (0,0,1)=1. Since x must be in the first or second place, the first parenthesis will give 1 only when y is in the 3rd place. Considering that the second bracket is always equal to 0, then F=1 is obtained due to the 1 in the first bracket. Thus, we found that y is in 3rd place. Finally, consider the 7th row of the table (1,0,1)=0. Here y=1 and for F=0 it is necessary to have z=0 and x=1, therefore, x is in the 1st place, and z is in the second.
Logic function F is given by the expression x/\ ¬y/\ (¬z\/ w).
The figure shows a fragment of the truth table of the function F containing All sets of arguments for which the function F true.
Determine which column of the function's truth table F each of the variables corresponds w, x, y, z.
Write the letters in your answer w, x, y, z in the order they come
their corresponding columns (first – the letter corresponding to the first
column; then the letter corresponding to the second column, etc.) Letters
In your answer, write in a row, put no separators between letters.
no need.
Demo version of the Unified State Examination USE 2017 – task No. 2
Solution:
A conjunction (logical multiplication) is true if and only if all statements are true. Therefore the variable X 1 .
Variable ¬y must match the column in which all values are equal 0 .
A disjunction (logical addition) of two statements is true if and only if at least one statement is true.
Disjunction ¬z\/y z=0, w=1.
Thus, the variable ¬z w corresponds to the column with variable 4 (column 4).
Answer: zyxw
Demo version of the Unified State Examination USE 2016 – task No. 2
Logic function F is given by the expression (¬z)/\x \/ x/\y. Determine which column of the truth table of the function F corresponds to each of the variables x, y, z.
In your answer, write the letters x, y, z in the order in which their corresponding columns appear (first - the letter corresponding to the 1st column; then - the letter corresponding to the 2nd column; then - the letter corresponding to the 3rd column) . Write the letters in the answer in a row; there is no need to put any separators between the letters.
Example. Let an expression x → y be given, depending on two variables x and y, and a truth table:
Then the 1st column corresponds to the variable y, and the 2nd column
corresponds to the variable x. In the answer you need to write: yx.
Solution:
1. Let's write the given expression in simpler notation:
¬z*x + x*y = x*(¬z + y)
2. Conjunction (logical multiplication) is true if and only if all statements are true. Therefore, so that the function ( F) was equal to one ( 1 ), each factor must be equal to one ( 1 ). Thus, when F=1, variable X must match the column in which all values are equal 1 .
3. Consider (¬z + y), at F=1 this expression is also equal to 1 (see point 2).
4. Disjunction (logical addition) of two statements is true if and only if at least one statement is true.
Disjunction ¬z\/y in this line will be true only if
- z = 0; y = 0 or y = 1;
- z = 1; y = 1
5. Thus, the variable ¬z corresponds to column with variable 1 (1 column), variable y
Answer: zyx
KIM Unified State Examination Unified State Exam 2016 (early period)– task No. 2
The logical function F is given by the expression
(x /\ y /\¬z) \/ (x /\ y /\ z) \/ (x /\¬y /\¬z).
The figure shows a fragment of the truth table of the function F, containing all sets of arguments for which the function F is true. Determine which column of the truth table of the function F corresponds to each of the variables x, y, z.
In your answer, write the letters x, y, z in the order in which their corresponding columns appear (first - the letter corresponding to the first column; then - the letter corresponding to the second column, etc.) Write the letters in the answer in a row, no separators There is no need to put it between letters.
R solution:
Let's write the given expression in simpler notation:
(x*y*¬z) + (x*y*z) + (x*¬y*¬z)=1
This expression is true when at least one of (x*y*¬z), (x*y*z), (x*¬y*¬z) equals 1. Conjunction (logical multiplication) is true if and only if when all statements are true.
At least one of these disjunctions x*y*¬z; x*y*z; x*¬y*¬z will be true only if x=1.
Thus, the variable X corresponds to the column with variable 2 (column 2).
Let y- variable 1, z- prem.3. Then, in the first case x*¬y*¬z will be true in the second case x*y*¬z, and in the third x*y*z.
Answer: yxz
The symbol F denotes one of the following logical expressions from three arguments: X, Y, Z. A fragment of the truth table of the expression F is given (see the table on the right). Which expression matches F?
| X | Y | Z | F |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
1) X ∧ Y ∧ Z 2) ¬X ∨ Y ∨¬Z 3) X ∧ Y ∨ Z 4) X ∨ Y ∧ ¬Z
Solution:
1) X ∧ Y ∧ Z = 1.0.1 = 0 (does not match on 2nd line)
2) ¬X ∨ Y ∨¬Z = ¬0 ∨ 0 ∨ ¬0 = 1+0+1 = 1 (does not match on the 1st line)
3) X ∧ Y ∨ Z = 0.1+0 = 0 (does not match on the 3rd line)
4) X ∨ Y ∧ ¬Z (corresponds to F)
X ∨ Y ∧ ¬Z = 0 ∨ 0 ∧ ¬0 = 0+0.1 = 0
X ∨ Y ∧ ¬Z = 1 ∨ 0 ∧ ¬1 = 1+0.0 = 1
X ∨ Y ∧ ¬Z = 0 ∨ 1 ∧ ¬0 = 0+1.1 = 1
Answer: 4
Given a fragment of the truth table of the expression F. Which expression corresponds to F?
| A | B | C | F |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
1) (A → ¬B) ∨ C 2) (¬A ∨ B) ∧ C 3) (A ∧ B) → C 4) (A ∨ B) → C
Solution:
1) (A → ¬B) ∨ C = (1 → ¬0) ∨ 0 = (1 → 1) + 0 = 1 + 0 = 1 (does not match on 2nd line)
2) (¬A ∨ B) ∧ C = (¬1 ∨ 0) ∧ 1 = (0+0).1 = 0 (does not match on the 3rd line)
3) (A ∧ B) → C = (1 ∧ 0) → 0 = 0 → 0 = 1 (does not match on 2nd line)
4) (A ∨ B) → C (corresponds to F)
(A ∨ B) → C = (0 ∨ 1) → 1 = 1
(A ∨ B) → C = (1 ∨ 0) → 0 = 0
(A ∨ B) → C = (1 ∨ 0) → 1 = 1
Answer: 4
A logical expression is given that depends on 6 logical variables:
X1 ∨ ¬X2 ∨ X3 ∨ ¬X4 ∨ X5 ∨ X6
How many different sets of variable values are there for which the expression is true?
1) 1 2) 2 3) 63 4) 64
Solution:
False expression only in 1 case: X1=0, X2=1, X3=0, X4=1, X5=0, X6=0
X1 ∨ ¬X2 ∨ X3 ∨ ¬X4 ∨ X5 ∨ X6 = 0 ∨ ¬1 ∨ 0 ∨ ¬1 ∨ 0 ∨ 0 = 0
There are 2 6 =64 options in total, which means true
Answer: 63
A fragment of the truth table of the expression F is given.
| x1 | x2 | x3 | x4 | x5 | x6 | x7 | F |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
Which expression matches F?
1) x1 ∨ x2 ∨ ¬x3 ∨ x4 ∨ ¬x5 ∨ x6 ∨ ¬x7
2) x1 ∨ ¬x2 ∨ x3 ∨ ¬x4 ∨ ¬x5 ∨ x6 ∨ x7
3) x1 ∧ ¬x2 ∧ x3 ∧ ¬x4 ∧ x5 ∧ ¬x6 ∧ x7
4) x1 ∧ x2 ∧ ¬x3 ∧ x4 ∧ ¬x5 ∧ x6 ∧ ¬x7
Solution:
1) x1 ∨ x2 ∨ ¬x3 ∨ x4 ∨ ¬x5 ∨ x6 ∨ ¬x7 = 0 + 1 + … = 1 (does not match on the 1st line)
2) x1 ∨ ¬x2 ∨ x3 ∨ ¬x4 ∨ ¬x5 ∨ x6 ∨ x7 = 0 + 0 + 0 + 0 + 0 + 1 + 0 = 1 (does not match on the 1st line)
3) x1 ∧ ¬x2 ∧ x3 ∧ ¬x4 ∧ x5 ∧ ¬x6 ∧ x7 = 1.0. ...= 0 (does not match on 2nd line)
4) x1 ∧ x2 ∧ ¬x3 ∧ x4 ∧ ¬x5 ∧ x6 ∧ ¬x7 (corresponds to F)
x1 ∧ x2 ∧ ¬x3 ∧ x4 ∧ ¬x5 ∧ x6 ∧ ¬x7 = 1.1.1.1.1.1.1 = 1
x1 ∧ x2 ∧ ¬x3 ∧ x4 ∧ ¬x5 ∧ x6 ∧ ¬x7 = 0. … = 0
Answer: 4
| x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | F |
| 0 | 1 | 1 | ||||||
| 1 | 0 | 1 | 0 | |||||
| 1 | 0 | 1 |
What expression can F be?
1) x1 ∧ ¬x2 ∧ x3 ∧ ¬x4 ∧ x5 ∧ x6 ∧ ¬x7 ∧ ¬x8
2) ¬x1 ∨ x2 ∨ x3 ∨ ¬x4 ∨ ¬x5 ∨ ¬x6 ∨ ¬x7 ∨ x8
3) ¬x1 ∧ x2 ∧ ¬x3 ∧ x4 ∧ x5 ∧ ¬x6 ∧ ¬x7 ∧ ¬x8
4) ¬x1 ∨ ¬x2 ∨ ¬x3 ∨ ¬x4 ∨ ¬x5 ∨ ¬x6 ∨ ¬x7 ∨ ¬x8
Solution:
1) x1 ∧ ¬x2 ∧ x3 ∧ ¬x4 ∧ x5 ∧ x6 ∧ ¬x7 ∧ ¬x8 = x1 . ¬x2. 0 . ... = 0 (does not match on 1st line)
2) ¬x1 ∨ x2 ∨ x3 ∨ ¬x4 ∨ ¬x5 ∨ ¬x6 ∨ ¬x7 ∨ x8 (corresponds to F)
3) ¬x1 ∧ x2 ∧ ¬x3 ∧ x4 ∧ x5 ∧ ¬x6 ∧ ¬x7 ∧ ¬x8 = … ¬x7 ∧ ¬x8 = … ¬1 ∧ ¬x8 = … 0 ∧ ¬x8 = 0 (does not match on 1- th line)
4) ¬x1 ∨ ¬x2 ∨ ¬x3 ∨ ¬x4 ∨ ¬x5 ∨ ¬x6 ∨ ¬x7 ∨ ¬x8 = ¬x1 ∨ ¬x2 ∨ ¬x3 … = ¬1 ∨ ¬x2 ∨ ¬0 .. = 1 (not matches on the 2nd line)
Answer: 2
Given is a fragment of the truth table for the expression F:
| x1 | x2 | x3 | x4 | x5 | x6 | x7 | F |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
Find the minimum possible number of different rows in the complete truth table of this expression in which the value x5 matches F.
Solution:
Minimum possible number of distinct rows in which the value x5 matches F = 4
Answer: 4
Given is a fragment of the truth table for the expression F:
| x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | F |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
Find the maximum possible number of distinct rows in the complete truth table of this expression in which the value x6 does not coincide with F.
Solution:
Maximum possible number = 2 8 = 256
The maximum possible number of different rows in which the value x6 does not match F = 256 – 5 = 251
Answer: 251
Given is a fragment of the truth table for the expression F:
| x1 | x2 | x3 | x4 | x5 | x6 | x7 | F |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
Find the maximum possible number of different rows of the complete truth table of this expression in which the value ¬x5 ∨ x1 coincides with F.
Solution:
1+0=1 – does not match F
0+0=0 – does not match F
0+0=0 – does not match F
0+1=1 – coincides with F
1+0=1 – coincides with F
2 7 = 128 – 3 = 125
Answer: 125
Each Boolean expression A and B depends on the same set of 6 variables. In the truth tables, each of these expressions has exactly 4 units in the value column. What is the minimum possible number of ones in the value column of the truth table of the expression A ∨ B?
Solution:
Answer: 4
Each Boolean expression A and B depends on the same set of 7 variables. In the truth tables, each of these expressions has exactly 4 units in the value column. What is the maximum possible number of ones in the value column of the truth table of the expression A ∨ B?
Solution:
Answer: 8
Each Boolean expression A and B depends on the same set of 8 variables. In the truth tables, each of these expressions has exactly 5 units in the value column. What is the minimum possible number of zeros in the value column of the truth table of the expression A ∧ B?
Solution:
2 8 = 256 – 5 = 251
Answer: 251
Each Boolean expression A and B depends on the same set of 8 variables. In the truth tables, each of these expressions has exactly 6 units in the value column. What is the maximum possible number of zeros in the value column of the truth table of the expression A ∧ B?
Solution:
Answer: 256
The Boolean expressions A and B each depend on the same set of 5 variables. There are no matching rows in the truth tables of both expressions. How many ones will be contained in the value column of the truth table of the expression A ∧ B?
Solution:
There are no matching rows in the truth tables of both expressions.
Answer: 0
The Boolean expressions A and B each depend on the same set of 6 variables. There are no matching rows in the truth tables of both expressions. How many ones will be contained in the value column of the truth table of the expression A ∨ B?
Solution:
Answer: 64
Each of the Boolean expressions A and B depends on the same set of 7 variables. There are no matching rows in the truth tables of both expressions. What is the maximum possible number of zeros in the value column of the truth table of the expression ¬A ∨ B?
Solution:
A=1,B=0 => ¬0 ∨ 0 = 0 + 0 = 0
Answer: 128
Each of the Boolean expressions F and G contains 7 variables. There are exactly 8 identical rows in the truth tables of the expressions F and G, and exactly 5 of them have a 1 in the value column. How many rows of the truth table for the expression F ∨ G contain a 1 in the value column?
Solution:
There are exactly 8 identical rows, and exactly 5 of them have a 1 in the value column.
This means that exactly 3 of them have a 0 in the value column.
Answer: 125
The logical function F is given by the expression (a ∧ ¬c) ∨ (¬b ∧ ¬c). Determine which column of the truth table of the function F corresponds to each of the variables a, b, c.
| ? | ? | ? | F |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |
In your answer, write the letters a, b, c in the order in which their corresponding columns appear.
Solution:
(a . ¬c) + (¬b . ¬c)
When c is 1, F is zero so the last column is c.
To determine the first and second columns, we can use the values from the 3rd row.
(a . 1) + (¬b . 1) = 0
Answer: ABC
The logical function F is given by the expression (a ∧ c)∨ (¬a ∧ (b ∨ ¬c)). Determine which column of the truth table of the function F corresponds to each of the variables a, b, c.
Based on the fact that when a=0 and c=0, then F=0, and the data from the second row, we can conclude that the third column contains b.
Answer: cab
The logical function F is given by x ∧ (¬y ∧ z ∧ ¬w ∨ y ∧ ¬z). The figure shows a fragment of the truth table of the function F, containing all sets of arguments for which the function F is true. Determine which column of the truth table of the function F corresponds to each of the variables x, y, z, w.
| ? | ? | ? | ? | F |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
In your answer, write the letters x, y, z, w in the order in which their corresponding columns appear.
Solution:
x ∧ (¬y ∧ z ∧ ¬w ∨ y ∧ ¬z)
x. (¬y . z . ¬w . y . ¬z)
Based on the fact that at x=0, then F=0, we can conclude that the second column contains x.
Answer: wxzy
Analysis of task 2 of the Unified State Exam 2017 in computer science from the demo version project. This is a task of a basic level of difficulty. Approximate time to complete the task is 3 minutes.
Tested content elements: ability to construct truth tables and logical circuits. Content elements tested on the Unified State Exam: statements, logical operations, quantifiers, truth of statements.
Task 2:
Logic function F is given by the expression x /\¬ y /\ (¬ z \/ w).
The figure shows a fragment of the truth table of the function F containing All F true.
Determine which column of the function's truth table F each of the variables corresponds w, x, y, z.
Write the letters in your answer w, x, y, z in the order in which the corresponding columns appear (first - the letter corresponding to the first column; then - the letter corresponding to the second column, etc.) Write the letters in the answer in a row, there is no need to put any separators between the letters.
Example. If the function were given by the expression ¬ x \/ y, depending on two variables: x And y, and a fragment of its truth table was given, containing All sets of arguments for which the function F true.
Then the first column would correspond to the variable y, and the second column is a variable x. The answer should have written: yx.
Answer: ________
x /\¬ y /\ (¬ z \/ w)
A conjunction (logical multiplication) is true if and only if all statements are true. Therefore the variable X 1 .
Thus, the variable x corresponds to the column with variable 3.
Variable ¬y the column containing the value must match 0 .
A disjunction (logical addition) of two statements is true if and only if at least one statement is true.
Disjunction ¬z\/w in this line will be true only if z=0, w=1.
Thus, the variable ¬z corresponds to column with variable 1 (1 column), variable w corresponds to the column with variable 4 (column 4).
