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Question

In a Boolean algebra B with respect to '+‘ and ’·', x' denotes the negation of xB. Then


A

x-x'=1 and x·x'=1

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B

x+x'=1 and x·x'=0

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C

x+x'=0 and x·x'=0

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D

x-x'=1 and x·x'=0

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Solution

The correct option is B

x+x'=1 and x·x'=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' is equal to 1. So x+x'=1.

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

Thus the correct relation is x+x'=1 and x·x'=0.

Hence, the correct option is B.


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