UGC NET CSE | October 2020 | Part 2 | Question: 37

Question

If $f(x)=x$ is my friend, and $p(x) =x$ is perfect, then correct logical translation of the statement “some of my friends are not perfect” is ______

• A. $\forall _x (f(x) \wedge \neg p(x))$
• B. $\exists _x (f(x) \wedge \neg p(x))$
• C. $\neg (f(x) \wedge \neg p(x))$
• D. $\exists _x (\neg f(x) \wedge \neg p(x))$

Answer 1

some of my friends are not perfect means there  are some (at least one ) persons which are my friends and not perfect

F(x)=x is my friend

P(x) = x is perfect  

now to represent some of my friends are not perfect use existential quantifier

∃x (f(x)∧¬p(x))  option B