For all $a$ and $b$ in $B$, $(a \times b) + a = a$.

Question

In the statements below, $B$ is a boolean algebra with $×$ and $+$ for binary operations.

3.) For all $a$ and $b$ in $B$, $(a ×b) + a = a$.

This is what I have as an answer. Can someone confirm or deny this logic? I am supposed to prove this. I am also having some trouble with Boolean algebra so I just wanted to make sure that I'm doing this right.

We can simplify ($a ×b) + a$ to $ab+a$. $=a(1+b)$
$=a×1$ because for all $b∈B, \ \ \ b+1=1$ because of the Universal Bound Law
$=a$

Answer 1

It looks good. (Except, LaTexify it next time! :-))