Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Boolean algebra rule?
I am trying to simplify something easy, but it has been a while and ive forgotten some rules:
(a + b) * (~b + c) =? (a * ~b) + (a * c) + (b * ~b) + (b * c) =? [a * (~b + c)] + [b * (~b + c)]
ok so far i have: a(~b+c) + b(~b+c)
there is a rule for this but i cant remember do both the (~b+c) just cancel out like in regular math or what is the rule?
The final answer should be: (a + c)
I know there are other steps that be be taken to simplify differently, however I want to know what to do when your in this situation: a(~b+c) + b(~b+c)
1 Answer
- ?Lv 71 decade agoFavorite Answer
In the previous step, you had:
(a * ~b) + (a * c) + (b * ~b) + (b * c)
At this point, if you wanted, you could just remove the (b * ~b) because that will always be 0. That would leave you with:
(a * ~b) + (a * c) + (b * c)
(I am also pretty sure that you cannot simplify (a + b) * (~b + c) into just (a + c). For example, if a = 0 and c = 1, then the result is 1 if b = 1, but the result is 0 if b = 0. Since the result depends on b, there's no way you can just simplify it away.)
