Question

Let a: ~ (p ∧ ~ r) v (~ q v s) and

b: (p v s) ↔ (q ∧ r).

If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.

विकल्प

• F, F

• T, T

• T, F

• F, T

Answer 1

F, F

Explanation:

Given, p, q → T and r, s → F

∴ a : ~ (p ∧ ~ r) v (~ q v s)

≡ ~ (T ∧ T) v (F v F)

≡ ~ (T) v (F)

≡ F v F

≡ F

and b : (p v s) ↔ (q ∧ r)

≡ (~ (p v s) v (q ∧ r)) ∧ ((p v s) v ~ (q ∧ r))

∴ p ↔ q ≡ (~ p v q) ∧ (p v ~ q)

≡ (~ (T v F) v (T ∧ F)) ∧ ((T v F) v ~ (T ∧ F))

≡ (F v F) ∧ (T v T)

≡ F ∧ T

≡ F