Boolean Algebra Problem ABCC'

Question

Hi I just want to ask the answer of this Boolean Algebra problem.. $$ABCC' + B + A'B $$

How to simplify that one?

Answer 1

I'll assume that, by $C'$, you mean $\bar{C}$, the negation of $C$. If that's the case, then the entire expression evaluates to just $B$.

Here's why: in the first term, $CC'$ is always false (it's the AND of a variable and its negation), so the entire first term is always false (it's the AND of $AB$ and false). So we only need to look at the last two terms.

Now, if $B$ is true then $B$ plus anything is true (the OR of anything and true is always true). If $B$ is false then the last term is false and the entire expression is false. Thus, the entire expression equals the value of $B$.

Answer 2

Since $CC′=0$ $$ABCC′=AB\cdot0=0$$ Also $$ B+A′B=B(1+A')=B\cdot 1=B $$ So $$ ABCC′+B+A′B=0+B=B $$