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I am revisiting Boolean algebra after a long while.

Can somebody help show me how to simplify the LHS to get the RHS?

$$abc * a'bc + (abc)' * (a'bc)'\quad = \quad \;b'+c'$$

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  • $\begingroup$ What is * and + ? AND and OR? $\endgroup$
    – Inquest
    Commented May 9, 2013 at 0:43
  • $\begingroup$ Yes, they are AND and OR. $\endgroup$ Commented May 9, 2013 at 0:44

1 Answer 1

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$$\color{blue}{\bf abc * a'bc} + (abc)' * (a'bc)'$$

Note: $$\color{blue}{\bf abc*a'bc} = abca'bc = (aa')bbcc = F*bc = \color{blue}{\bf F}$$

So we simplify what remains: $$\color{blue}{\bf F} + (abc)' * (a'bc)' = (abc)' * (a'bc)'$$ $$ = (a'+b'+c')*(a + b' + c')\tag{ by Demorgan's.}$$

$$ = (b' + c')+ (a' * a)\tag{Distributive law}$$ $$ = b' + c' + F $$ $$= b' + c'$$

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  • $\begingroup$ I only shave once a week, but the beard and moustache never really grow in like I'd like! :-) $\endgroup$
    – Amzoti
    Commented May 9, 2013 at 4:26
  • $\begingroup$ Hello, @Babak! Did you sleep well? $\endgroup$
    – amWhy
    Commented May 9, 2013 at 4:28
  • $\begingroup$ @amWhy: Oh yes Amy. If we could make levels for sleeping exactly the same as we get + up to 250 up voting every day; I got 210 for that last night. :D $\endgroup$
    – Mikasa
    Commented May 9, 2013 at 4:33
  • $\begingroup$ @amWhy: So; go sleep. You brain needs it. Angels are all waiting to greet you in Heaven with all you became satisfied. I'll be waiting here to see you.... ;-) $\endgroup$
    – Mikasa
    Commented May 9, 2013 at 4:41

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