Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I can work out what the expression simplifies to and can show the equivalence with a truth table, but I don't know the law (or sequence of laws) that need to be applied to show this formally.

This is the expression: ¬X OR (Y AND X) where ¬ is NOT.
and it simplifies to: ¬X OR Y

WolframAlpha also shows this when expressing it in CNF:

This is part of a homework question and just need help understanding how this stage works. I've read through the laws and searched the Internet and any law I try to apply doesn't produce the correct expression.

share|cite|improve this question
up vote 2 down vote accepted

by distributivity you get $\neg X \lor (Y \land X) \equiv (\neg X \lor Y) \land (\neg X \lor X)$. Now $\neg X \lor X \equiv \top$ (true) and so the term simplifies to $\neg X \lor Y$.

share|cite|improve this answer
(~X OR Y) AND (~X OR X)
(~X OR Y) AND (1)
(~X OR Y)
share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.