CODEWITHSUNDEEP
booleanboolean-logicboolean-algebra
Kaushik Evani
Kaushik Evani

Reputation: 1224

How do I simplify(expand) this Boolean expression?

Expression - (A OR B OR C OR D) AND (!B AND !D)

I know that with distributive property, it holds that (a OR b) AND (c OR d) = (a AND c) OR (a AND d) OR (b AND c) or (b AND d) but I'm not sure how it will work if the second group has an AND

Steps in the answer would help.

Upvotes: 1

Views: 225

Answers (1)

Patrick87
Patrick87

Reputation: 28332

Something like this perhaps?

  (A OR B OR C OR D) AND (!B AND !D)
= (A OR B OR C OR D) AND !(B OR D)
= ((A OR C) OR (B OR D)) AND !(B OR D)
= ((A OR C) AND !(B OR D)) OR ((B OR D) AND !(B OR D))
= (A OR C) AND !(B OR D) OR false
= (A OR C) AND !(B OR D)

That seems like it's going to be minimal since each variable appears once and there are no apparent contradictions or tautologies.

Upvotes: 1

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