Discrete Math/Truth Tables?

Let's restate:

(p v q) v (p v r):

Since you can transform it equivalently into: (p v q v r), its interpretation (restatement) is:

"at least one of p, q, r holds true"

This instantly implies that "if r is NOT true, then necessarily either p or q is true"

And since the IF...THEN structure is an implication, this is obviously written down as (i.e. is a restatement of):

¬r -> (p v q)


So:


"at least one of p, q, r holds true" IMPLIES "if r is NOT true, then necessarily either p or q is true"

is now backwards written down symbolically as:

[ (p v q) v (p v r) ] -> [ ¬r -> (p v q) ]


and the proof is complete....Show more