Question

The relation “is a subset of” on the power set $P\left(A\right)$ of a set $A$ is

• A. Symmetric
• B. Antisymmetric
• C. Equivalency relation
• D. None of these

Answer 1

The correct option is B

Antisymmetric

Explanation for the correct answer:

Compute the required relation:

$A\subset A$

$(A,A)\in R$ is reflexive

$(a,b)\in R$

$(b,a)\in R$

It is symmetric.

$\Rightarrow$$$\begin{gathered} A\subset B \\ B\subset A \end{gathered}$$

The above expressions are possible if $A=B$.

Thus the relation is antisymmetric.

Hence, option $\left(B\right)$ is the correct answer.