Question

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

• A. Symmetric only
• B. Equivalence relation
• C. Reflexive only
• D. None of these

Answer 1

The correct option is A Symmetric only

Let the universal set be

$u=\left\{a,b,c,d,.......z\right\}$

New consider the relation inclusion of a subset

(i) every set is a subset as itself

Thus set $\left\{a\right\}\subset \left\{a\right\}$

hence, respectively is satisfied.

(ii) Now considered the let $a$ and $a,b$

Here $\left\{a\right\}\subset \left\{a,b\right\}$

but $\left\{a,b\right\}\subset \left\{a\right\}$

Therefore it is not symmetric

Hence the relation inclusion at a subset is not an equivalence relation.