In a boolean algebra (B) with respect to (' +' ) and ('.',)... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

In a boolean algebra $B$ with respect to $' +'$ and $'.',$ $x'$ denotes the negation of $x\in B$ . Then

A

$x - x' = 1$ and $x \cdot x' = 1$

B

$x + x' = 1$ and $x \cdot x' = 0$

C

$x + x' = 0$ and $x \cdot x' = 1$

D

$x + x' = 0$ and $x \cdot x' = 0$

Answer

$x + x' = 1$ and $x \cdot x' = 0$

Explanation

Solution

By the complement law, $x+x=1$ and $x.x=0$