- #1
Of Mike and Men
- 54
- 3
Hey everyone, I am in a discrete math course, and I was reading pre-reading the textbook (Discrete Mathematics with Applied Applications by Epp 4th Ed.), but didn't understand their example, I don't understand, specifically, the distributive portion. I don't see how they distributed it like that, if someone could expound on it, it'd be great.
Verify ~(~p ∧ q) ∧ (p ∨ q) ≡ p
~(~p ∧ q ) ∧ (p ∨ q) ≡ (~(~p) ∨ ~q) ∧ (p∨q) De Morgan's Laws
≡(p ∨ ~q) ∧ (p ∨ q) Double Negative Law
≡p ∨ (~q ∧ q) Distributive Law (the part I don't understand)
≡ p ∨ ℂ Negation Law
≡ p Identity Law
Verify ~(~p ∧ q) ∧ (p ∨ q) ≡ p
~(~p ∧ q ) ∧ (p ∨ q) ≡ (~(~p) ∨ ~q) ∧ (p∨q) De Morgan's Laws
≡(p ∨ ~q) ∧ (p ∨ q) Double Negative Law
≡p ∨ (~q ∧ q) Distributive Law (the part I don't understand)
≡ p ∨ ℂ Negation Law
≡ p Identity Law