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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:
http://www.wolframalpha.com/input/?i=not+X+or+%28Y+and+X%29

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.

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2 Answers 2

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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 $\neg X \lor Y$.

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~X OR (Y AND X)
(~X OR Y) AND (~X OR X)
(~X OR Y) AND (1)
(~X OR Y)
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