∀x,p(x) is read asFor every x∈U,p(x) isfalseFor every x∈p(x) is trueFor every x∈U,p(x) is trueFor every p(x) is true

What are the truth values of these statements? a) ∃!xP(x)→∃xP(x) b) ∀x P(x) → ∃!xP(x) c) ∃!x¬P(x)→¬∀xP(x)

Show that ∃x(P(x)∨Q(x)) and ∃xP(x)∨∃xQ(x) are logically equivalent

The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people. ans. ∃x(C(x) ∧ F (x)) ∀x(C(x) ∧ F (x)) ∀x(C(x) → F (x)) ∃x(C(x) → F (x))

Let Ω be the sample space and A⊆Ω be an event. Given below are two statements:(S1): If P(A)=0, then A=ϕ(S2): If P(A)=1, then A=ΩThenonly (S1) is trueonly (S2) is trueboth (S1) and (S2) are trueboth (S1) and (S2) are false

Universal Quantifier