Question

Which of the following is not true for any two statements p and q?

Options

• ~[p ∨ (~ q)] ≡ ~ p ∧ q

• (p ∨ q) ∨ (~ q) is a tautology

• ~(p ∧ ~ p) is a tautology

• ~(p ∨ q) ≡ ~ p ∨ ~ q

Answer 1

~(p ∨ q) ≡ ~ p ∨ ~ q

Explanation:

~(p ∨ q) ≡ ~ p ∨ ~ q is not true as it contradicts De Morgan's law.