Q40,paper2,J13. The truth value of the statements :

∃!xP(x) ->∃xP(x) and

∃!x`P(x) ->`∀xP(x), (where the notation ∃!xP(x)

denotes the proposition “There exists a unique x such that P(x) is true”) are :

(A) True and False

(B) False and True

(C) False and False

(D) True and True

Answer D

Statement 1.There exists  a unique x,where p(x) is true. Implies that there exists a x where p(x) is true.

Statement 2. There exists a unique x where p(x) is false.implies that ‘not for all x. p(x) is true.’

Statement 2 is true. Where as statement 1 is also true.

Answer D.