made easy test series

Question

Consider the following predicates:

S(x): x is a student

GATE(x,y): x has written gate in stream y.

Which of the following is equivalent predicate logic for the statement : “There doesnt exist a student who has written GATE in every stream.”

(a)$\exists y\exists x[S(x)\Lambda \sim GATE(x,y)]$

(b)$\forall y\exists x[\sim S(x)V \sim GATE(x,y)]$

(c)$\forall x\exists y[\sim S(x)V \sim GATE(x,y)]$

(d)$\exists y\exists x[\sim S(x)\Lambda \sim GATE(x,y)]$

Comments

Shobhit Joshi

Thanks..got it now :)

jatin khachane 1

If x isnt a student, then it doesnt matter whether it is true or false since the statement only speaks of students and not of non-students..so it may be true or may not be.

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@jatin khachane 1 if there is no student, then "There doesn't exist a student who has written GATE in every stream", this is also satisfied. Isn't it ?

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yes @Shobhit Joshi

 you right if not student then it may be true / false