# Is this boolean expression reducible?

I have this boolean expression: F1 = a1'a2' + a1a2'.

Could it be reduced even more?

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Yes. If you can't just see it, write out a logic table and see what you get. – The Photon Dec 22 '12 at 18:55
looks like homework – Erion Dec 23 '12 at 10:01
@Erion Not exactly. – Billie Dec 23 '12 at 14:07

Yes, factor out the a2'. You should see something interesting with what happens to a1.

When you factor out a2', you get a2'(a1' + a1)

The statement a1' + a1 means (a1 or NOT a1). It should be obvious that this is ALWAYS true and thus can be removed from the logic statement. This leaves you with F1 = a2'

In general, the tools for reducing logic expressions that I know of are algebraic manipulation (deMorgan's Laws, distributive property, etc.), Karnaugh Maps, and the Quine McCluskey Algorithm.

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Thanks! You're right. on which law have you based? how did you know this answer? – Billie Dec 22 '12 at 19:04
To be honest, I just saw it immediately... It's kind of a distributive property I guess. Let me see if I can find some more formal resources about this. – NickHalden Dec 22 '12 at 19:05
Thank you. p.s. , you meant to a1'a2' + a1, am I right? – Billie Dec 22 '12 at 19:07
@user1798362, sorry you are still a little off track. – The Photon Dec 22 '12 at 19:09
Just think of it in words: Something is true if a2' is true and a1 is true; or its true if a2' is true and a1 is not true. So does a1 really matter to the final result? – The Photon Dec 22 '12 at 19:10