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

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