Correctness of Proof by Refutation

Question

I am trying to solve the following by proof by refutation:

A or B 1.
NOT A or I 2.
NOT B or T 3.
NOT I 4.
NOT T 5.

Where the goal is to prove a contradiction.

My approach has been:

NOT A 6. [2+4]
NOT B 7. [3+5]
CONTRADICTION 8. [1+6+7]

By the logic that:

(A OR B) AND NOT A AND NOT B IMPLY CONTRADICTION

The book however solves it by deriving:

A [1+7]

Ie: Using NOT B together with A OR B

And then calling a contradiction by A AND NOT A.

Would my strategy be acceptable?

score 2 · Accepted Answer · answered Jun 06 '14 at 19:45

2

$\lnot (A \lor B) \Leftrightarrow (\lnot A \land \lnot B)$.

answered Jun 06 '14 at 19:45

Mauro ALLEGRANZA

Ok thanks, so I can simply assume De Morgan's Law without having to justify further correct? – MrD Jun 06 '14 at 19:55
1

@DarioP - it depends on the set of rules you are allowed to use ... How you justify step 6 ? You have used : from $P \lor Q$ and $\lnot P$, derive $Q$ (this is Disjunctive syllogism ). – Mauro ALLEGRANZA Jun 06 '14 at 20:08

1 Answers1