Question

Which of the following is not true for two non-empty sets A and B?

• A. If A $\subset$ B and A $\ne$ B, then A is called superset of B.
• B. For every set A, empty set $\varphi$ and A itself, are the subsets.
• C. If A $\subseteq$ B and B $\subseteq$ A, then A = B.
• D. If A $\subset$ B and A $\ne$ B, then B is not a subet of A.

Answer 1

The correct option is A If A $\subset$ B and A $\ne$ B, then A is called superset of B.

We can see that all the three options viz., option A, B, and C are true by the definition of subsets.
Now, if A and B are two non-empty sets and A $\subset$ B and A $\ne$ B, then A is called the proper subset of set B, and B is called the superset of set A.
Therefore, option D is not true and hence it is the only correct option out of the given options.