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Discrete Math/Truth Tables?
(p v q) v (p v r) -> ¬r --> (p v q)
The goal is to try and prove ¬r --> (p v q) using Statement/Reason table. I really have no idea how to even start
1 Answer
- O(n)Lv 53 years ago
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.