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mathboolean-logicalgebraboolean-algebra

Simplifying this boolean algebra

Is it possible to simplify this boolean algebra? I want to remove the redundancy of using twice the X variable, but can't seem to see a way how.

(X AND Y) OR NOT(X AND Z)

Thanks in advance!

Solution

  • It's equivalent to

    (X AND Y) OR (NOT X OR NOT Z)

    which is equivalent to

    (X AND Y) OR NOT X OR NOT Z

    which is equivalent to

    (X OR NOT X OR NOT Z) AND (Y OR NOT X OR NOT Z)

    which is equivalent to

    (TRUE) AND (Y OR NOT X OR NOT Z)

    (since X or NOT x == true and TRUE OR Z == true)

    which is equivalent to

    Y OR NOT X OR NOT Z

    You can also use a K-map to find an equivalent logical expression, but those are harder to type :)