Question

$a,b,c\in B$,If $B$ is boolean algebra $a,b,c\in B,thena(a+b)=$

• A. $a$
• B. $b$
• C. $1$
• D. $a\text{'}$

Answer 1

The correct option is A

$a$

Explanation for the correct option:

Finding the value of $a\left(a+b\right):$

Given, $a,b,c\in B$

then, $$\begin{gathered} a.(a+b)=\left(a+0\right).\left(a+b\right) \\ \left[thereforea+\left(b.c\right)=\left(a+b\right).\left(a+c\right)\right] \\ \mathbf{=}\mathit{a}\mathbf{+}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{b}\mathbf{)} \\ \mathbf{=}\mathit{a}\mathbf{+}\mathbf{(}\mathbf{b}\mathbf{.}\mathbf{0}\mathbf{)} \\ =a+0 \\ \mathbf{=}\mathit{a} \end{gathered}$$ ( by using multiplicative law)

Hence, option(A) is correct.