Question

In a Boolean algebra $B$ with respect to '$+$‘ and ’$·$', $x\text{'}$ denotes the negation of $x\in B$. Then

• A. $x-x\text{'}=1$ and $x·x\text{'}=1$
• B. $x+x\text{'}=1$ and $x·x\text{'}=0$
• C. $x+x\text{'}=0$ and $x·x\text{'}=0$
• D. $x-x\text{'}=1$ and $x·x\text{'}=0$

Answer 1

The correct option is B

$x+x\text{'}=1$ and $x·x\text{'}=0$

Explanation for the correct option.

Find the correct relation between $x$ and its negation.

By the complement law in Boolean algebra, it can be said that the summation of $x$ and its negation $x\text{'}$ is equal to $1$. So $x+x\text{'}=1$.

By the complement law in Boolean algebra, it can be said that the product of $x$ and its negation $x\text{'}$ is equal to $0$. So $x·x\text{'}=0$.

Thus the correct relation is $x+x\text{'}=1$ and $x·x\text{'}=0$.

Hence, the correct option is B.