Question

The Cartesian product of two sets $P$ and $Q$, i.e.,$P\times Q=\varnothing$, if

• A. either $P$ or $Q$ is the null set.
• B. neither $P$ nor $Q$ is the null set
• C. Both (A) and (B)
• D. None of these

Answer 1

The correct option is A

either $P$ or $Q$ is the null set.

Explanation for the correct option:

The cartesian product $P\times Q$ is the set of all ordered pairs of elements from $P$ and $Q$; that is

$P\times Q=\{\left(p,q\right):p\in P,q\in Q\}$

So, $P\times Q=\varnothing$ is only possible when either $P$ or $Q$ is the null set.

Therefore, the correct answer is option (A)