Q19,Paper 2,J14.

The notation ∃!xP(x) denotes the proposition “there exists a unique x

such that P(x) is true”. Give the truth values of the following statements :

I. ∃!xP(x)→∃xP(x)

II. ∃!x¬P(x) →¬∀xP(x)

(A) Both I & II are true.

(B) Both I & II are false.

(C) I – false, II – true

(D) I – true, II – false

Answer A.

Statement 1.

There exists a unique x where p(x) is true implies there exists a x where  where p(x) is true.

Statement 2.

There exists a unique x where p(x) is not true. Implies not for every x,p(x) is true.

Both are true.