UGC NET CSE | September 2013 | Part 2 | Question: 24

Question

The quantification $\exists ! x P(x)$ denotes the proposition “There exists a unique x such that P(x) is true”, express he quantification using universal and existential quantifications and logical operators?

• A. $\exists x P(x) \vee \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$
• B. $\forall x P(x) \wedge \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$
• C. $\exists x P(x) \wedge \forall x \forall y ((P(x) \wedge P(y)) \rightarrow x=y)$
• D. $\exists x P(x) \wedge \forall x \forall y ((P(x) \vee P(y)) \rightarrow x=y)$

Answer 1

Ans is c .

∃xP(x)∧∀x∀y((P(x)∧P(y))→x=y)

Comments

Can u explain it ??

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yes, explain it please.