Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Suppose the predicate F(x, y, t) is used to r...
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Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?
- a)Everyone can fool some person at some time
- b)No one can fool everyone all the time
- c)Everyone cannot fool some person all the time
- d)No one can fool some person at some time
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
The predicate F(x, y, t) represents the statement that person x can fool person y at time t. Here, x, y and t are variables. This means that the statement can be true or false based on what values are assigned to x, y and t.
Now, let's look at the given formula xyt(F(x, y, t)). This formula is saying that there exists some value of x, y and t such that F(x, y, t) is true. In other words, there exists a person x who can fool a person y at time t.
Let's analyze each option to see which one expresses the meaning of the formula best.
Option A: Everyone can fool some person at some time
This option is saying that for every person x, there exists some person y and some time t such that x can fool y at time t. This is not equivalent to the given formula because the formula only says that there exists some value of x, y and t such that x can fool y at time t. It does not say that this is true for every x, y and t.
Option B: No one can fool everyone all the time
This option is saying that there does not exist a person x who can fool every person y at all times. This is equivalent to the given formula because the formula is saying that there exists some value of x, y and t such that x can fool y at time t. This means that there does not exist a person who can fool every other person at all times.
Option C: Everyone cannot fool some person all the time
This option is saying that for every person x, there exists some person y and some time t such that x cannot fool y at time t. This is not equivalent to the given formula because the formula only says that there exists some value of x, y and t such that x can fool y at time t. It does not say that this is false for every x, y and t.
Option D: No one can fool some person at some time
This option is saying that there does not exist a person x who can fool some person y at some time t. This is not equivalent to the given formula because the formula is saying that there exists some value of x, y and t such that x can fool y at time t. It does not say that this is true for every x, y and t.
Therefore, option B is the best expression of the given formula because it is equivalent to the formula.
The predicate F(x, y, t) represents the statement that person x can fool person y at time t. Here, x, y and t are variables. This means that the statement can be true or false based on what values are assigned to x, y and t.
Now, let's look at the given formula xyt(F(x, y, t)). This formula is saying that there exists some value of x, y and t such that F(x, y, t) is true. In other words, there exists a person x who can fool a person y at time t.
Let's analyze each option to see which one expresses the meaning of the formula best.
Option A: Everyone can fool some person at some time
This option is saying that for every person x, there exists some person y and some time t such that x can fool y at time t. This is not equivalent to the given formula because the formula only says that there exists some value of x, y and t such that x can fool y at time t. It does not say that this is true for every x, y and t.
Option B: No one can fool everyone all the time
This option is saying that there does not exist a person x who can fool every person y at all times. This is equivalent to the given formula because the formula is saying that there exists some value of x, y and t such that x can fool y at time t. This means that there does not exist a person who can fool every other person at all times.
Option C: Everyone cannot fool some person all the time
This option is saying that for every person x, there exists some person y and some time t such that x cannot fool y at time t. This is not equivalent to the given formula because the formula only says that there exists some value of x, y and t such that x can fool y at time t. It does not say that this is false for every x, y and t.
Option D: No one can fool some person at some time
This option is saying that there does not exist a person x who can fool some person y at some time t. This is not equivalent to the given formula because the formula is saying that there exists some value of x, y and t such that x can fool y at time t. It does not say that this is true for every x, y and t.
Therefore, option B is the best expression of the given formula because it is equivalent to the formula.
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Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?a)Everyone can fool some person at some timeb)No one can fool everyone all the timec)Everyone cannot fool some person all the timed)No one can fool some person at some timeCorrect answer is option 'B'. Can you explain this answer?
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Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?a)Everyone can fool some person at some timeb)No one can fool everyone all the timec)Everyone cannot fool some person all the timed)No one can fool some person at some timeCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?a)Everyone can fool some person at some timeb)No one can fool everyone all the timec)Everyone cannot fool some person all the timed)No one can fool some person at some timeCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?a)Everyone can fool some person at some timeb)No one can fool everyone all the timec)Everyone cannot fool some person all the timed)No one can fool some person at some timeCorrect answer is option 'B'. Can you explain this answer?.
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