## Boolean Simplification [closed]

Hi,

I have a boolean simplification problem that's already been solved.. but I'm having a hard time understanding one basic thing about it.. the order in which it was solved.

The problem is simplifying this equation:

Y = ¬A¬B¬C + ¬AB¬C + A¬B¬C + A¬BC + ABC


The solution is:

Y = ¬A¬B¬C + ¬AB¬C + A¬B¬C + A¬BC + ABC
= ¬A¬B¬C + ¬AB¬C + A¬B¬C + A¬BC + A¬BC + ABC (idempotency for A¬BC)
= ¬A¬C(¬B + B) + A¬B(¬C + C) + AC(¬B + B)
= ¬A¬C + A¬B + AC


The way I solved it is:

Y = ¬A¬B¬C + ¬AB¬C + A¬B¬C + A¬BC + ABC
= ¬A¬B¬C + ¬AB¬C + ¬A¬B¬C + A¬B¬C + A¬BC + ABC (idempotency for ¬A¬B¬C)
= ¬A¬C(¬B + B) + ¬B¬C(¬A + A) + AC(¬B +B)
= ¬A¬C + ¬B¬C + AC


So how do I know which term to use the law of idempotency on? Thanks.

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Your answer is equivalent to the given one. There's no reason to prefer one over the other. – Eric Tressler Oct 6 2010 at 22:18
This looks like a homework problem, which isn't the point of the website. Please look at the FAQ. – Ryan Budney Oct 6 2010 at 22:53