geeksforgeeks

Question

Let S(x) be the predicate "x is a student",T(x) be the predicate "x is a teacher"and Q(x,y) be the predicate "x has asked y a question" where the domain consists of all people associated with the school. Use quantifiers to express the statement.

"Some student has never been asked a question by a Teacher" 

A	∃x(S(x) ∨ ∀y(T(y)) → ¬ Q(x,y)))
B	¬∀x(S(x) ∨ ∀y(T(y)) → ¬ Q(y,x)))
	∃x(S(x) ∧ ∀y(T(y)) → ¬ Q(y,x)))
	¬∀x(S(x) ∧ ∀y(T(y)) → Q(x,y)))

 

All options seems to be wrong to me. But the last one looked closest. Can anyone pls help me in understanding this?

What I am up to –

As far as i know, with ∃, we always use ‘^’ and with ∀ we use ‘→ ’.

So, The statement would be translated as-

∃x∀y S(x) ∧ T(y) ∧ ¬Q(y,x)

=> ∃x∀y ¬( ¬( S(x) ∧ T(y) ) ∨ Q(y,x) )

=> ¬ ∀x∃y ( ( S(x) ∧ T(y) ) → Q(y,x) )  [ ¬P v Q = P→Q ]

None of the options are matching….

Comments

your logic is wrong it is interpreted as

if x is some student and y is all teacher then all y teacher never asked some x student a question

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Why do you feel that. Think again. My logic says-

There exists some x {x being student} such that for all y {y being teacher}, y has never asked a question to x.

that is-> some student has never been asked a question by any teacher.

if you still feel its wrong then probably i am not able to change my mind. Can you pls give me your solution. what do you think should be the answer and why?