Question

The relation $\le$ on numbers has the following properties.

(i) $a\le a\forall a\in R$ (Reflexivity)

(ii) If $a\le b$ and $b\le a$ then $a=b\forall a,b\in R$ (Antisymmetry)

(iii) If $a\le b$ and $b\le c$ then $a\le c\forall a,b\in R$ (Transitivity)

Which of the above properties does the relation $\subset$on $p\left(A\right)$ has?

• A. (i) and (ii)
• B. (i) and (iii)
• C. (ii) and (iii)
• D. (i), (ii) and (iii)

Answer 1

The correct option is D

(i), (ii) and (iii)

Explanation for the correct option:

Classify the relation $\subset$according to the given relation:

(i) $x\subset x$ (because every set is a subset of itself. So, Reflexivity is true.)

(ii) If $x\subset y$ and $y\subset x$, then $x=y$. [So, Antisymmetric holds good.]

(iii) $x\subset y,y\subset z$ $\Rightarrow x\subset z$ [So, Transitivity holds good.]

Hence, option $D$ is the correct answer.