Q:

Use a truth table to verify the first De Morgan law (p ∧ q)’ ≡ p’ ∨ q’.

Accepted Solution

A:
Answer:(p ∧ q)’ ≡ p’ ∨ q’Step-by-step explanation:First, p and q have just four (4) possibilities, p∧q is true (t) when p and q are both t.p ∧    qt t tt f ff f tf f fnext step is getting the opposite(p∧q)'     f     t     t     tThen we get p' V q', V is true (t) when the first or the second is true.p' V  q' f  f  f f  t  t t  t  f t  t  tLet's compare them, ≡ is true if the first is equal to the second one.(p∧q)'   ≡     (p' V q')     f              f     t              t     t              t     t              tBoth are true, so(p ∧ q)’ ≡ p’ ∨ q’