Question

show that p belongs to q or

Answer 1

Answer:

Show that (p ∧ q) → (p ∨ q) is a tautology

The first step shows: (p ∧ q) → (p ∨ q) ≡ ¬(p ∧ q) ∨ (p ∨ q)

I've been reading my text book and looking at Equivalence Laws. I know the answer to this but I don't understand the first step.

How is (p ∧ q)→ ≡ ¬(p ∧ q)?

If someone could explain this I would be extremely grateful. I'm sure its something simple and I am overlooking it.

The first thing I want to do when seeing this is

(p ∧ q) → (p ∨ q) ≡ ¬(p → ¬q)→(p ∨ q)

but the answer shows:

¬ (p ∧ q) ∨ (p ∨ q) (by logical equivalence)

Hope my answer will help you...

Answer 2

Step-by-step explanation:

x-> y = ~xvy

p^q -> pvq

= ~(p^q)v(pvq)

= ~pv~qvp vq

= (~pvp) v(~q vq)

= TvT = T

Always x v ~x results true

hence tautology,

hope my explanation is helpful to you - naimabanu055