Question

With reference to a universal set, the inclusion of a subset in another, is relation which is

• A. symmetric only
• B. equivalence
• C. reflexive only
• D. None of these

Answer 1

Answer: (C)

Let the universal set be
$U=\left\{x_1,x_2,x_3\dots x_n\right\}$
We know every set is a subset of itself.
Therefore, inclusion of a subset is reflexive Now the elements of the set $\left\{x_1\right\}$ are included in the set $\left\{x_1,x_2\right\}$ but converse is not true i.e.,
$\left\{x_1\right\}\subset \left\{x_1,x_2\right\}\text{ but }\left\{x_1,x_2\right\}\not\subset \left\{x_1\right\}$
Hence, the inclusion of a subset is not symmetric.
Thus, the inclusion of a subset is not an equivalence relation.