Question

Which of the following sets is a non-empty set?

• A. {$x:x$ is a natural number, $x$ < 8 and $x$ > 12}
• B. {$y:y$ is a point common to any two parallel lines}
• C. {$q:q$ $\in$ I, $q$ > -1 and $q$ > 8}
• D. {$p:p$ $\in$ I, $p^2$ < 0}

Answer 1

The correct option is C {$q:q$ $\in$ I, $q$ > -1 and $q$ > 8}

A natural number can not be less than 8 and more than 12 at the same time. So, the set given in option (a) is the null set.

Two parallel lines do not meet and hence, they can never have a common point. So, the set given in option (b) is the null set.

An integer can be greater than - 1 and 8 at the same time.

So, the set given in option (c) is not the null set.

The square of any integer cannot be less than zero. So, the set given in option (d) is the null set.