cse 260 exam 1

Identity Laws

prepositions

p∧T≡ p

Only true or false (not both)

q then p

¬q →¬p

¬p →¬q

Neither contradiction nor tautology

p∨T≡ p

p∨p ≡ p

p∨q ≡ q ∨p

p∨(q ∧r)≡ (p∨q)∧(p∨r)

Not p

p and q

p or q

If p then q. Only false when p is true and q is false. p implies q

Exclusive or. True only when exactly one of p or q is true

IFF. True when both have the same truth values

Always false

Always true

¬(¬p)≡ p

(p∨q)∨r ≡ p∨(q ∨r)

¬(p∧q)≡¬p∨¬q

p∨(p∧q)≡ p

p∨¬p ≡T

Assume p, p → q, therefore q (tautology)

¬q, p → q, therefore ¬p

p → q, q → r, therefore p → r

p∨q, ¬p, therefore q

p, therefore p∨q

p∧q, therefore p

p, q, therefore p∧q

p∨q, ¬p∨r, therefore q ∨r