Question

Let $S$ be non-empty subset of $R$ then consider the following statement

"Every number $xϵS$ is an even number."

Negation of the statement will be

• A. There is no number $xϵS$ which is even
• B. There exists a number $xϵS$ which is not even
• C. There exists a number $xϵS$ which is odd
• D. ($B$) and ($C$) both

Answer 1

The correct option is D ($B$) and ($C$) both

The given statement implies $x$ in the set $S$ is always even. The negation of this means there exists $x$ in $S$ which is not even, or which is odd.

So, option $D$ is correct.