GATE 2010
March 13, 2025GATE 2010
March 13, 2025GATE 2010
| Question 30 |
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))?
| Everyone can fool some person at some time | |
| No one can fool everyone all the time | |
| Everyone cannot fool some person all the time
| |
| No one can fool some person at some time |
Question 30 Explanation:
F(x,y,t) ⇒ Person ‘x’ can fool person ‘y’ at time ‘t’.
For better understanding propagate negation sign outward by applying Demorgan’s law.
∀x∃y∃t(¬F(x, y, t)) ≡ ¬∃x∀y∀t(F(x,y,t))
Now converting ¬∃x∀y∀t(F(x,y,t)) to English is simple.
¬∃x∀y∀t(F(x,y,t)) ⇒ There does not exist a person who can fool everyone all the time.
Which means “No one can fool everyone all the time”.
Hence, Option (B) is correct.
For better understanding propagate negation sign outward by applying Demorgan’s law.
∀x∃y∃t(¬F(x, y, t)) ≡ ¬∃x∀y∀t(F(x,y,t))
Now converting ¬∃x∀y∀t(F(x,y,t)) to English is simple.
¬∃x∀y∀t(F(x,y,t)) ⇒ There does not exist a person who can fool everyone all the time.
Which means “No one can fool everyone all the time”.
Hence, Option (B) is correct.
Correct Answer: B
Question 30 Explanation:
F(x,y,t) ⇒ Person ‘x’ can fool person ‘y’ at time ‘t’.
For better understanding propagate negation sign outward by applying Demorgan’s law.
∀x∃y∃t(¬F(x, y, t)) ≡ ¬∃x∀y∀t(F(x,y,t))
Now converting ¬∃x∀y∀t(F(x,y,t)) to English is simple.
¬∃x∀y∀t(F(x,y,t)) ⇒ There does not exist a person who can fool everyone all the time.
Which means “No one can fool everyone all the time”.
Hence, Option (B) is correct.
For better understanding propagate negation sign outward by applying Demorgan’s law.
∀x∃y∃t(¬F(x, y, t)) ≡ ¬∃x∀y∀t(F(x,y,t))
Now converting ¬∃x∀y∀t(F(x,y,t)) to English is simple.
¬∃x∀y∀t(F(x,y,t)) ⇒ There does not exist a person who can fool everyone all the time.
Which means “No one can fool everyone all the time”.
Hence, Option (B) is correct.