Let $T$ be a set of $n$ elements. It is defined that
- a relation $R$ on $T$ is symmetric if $(a, b) \in R$ then $(b, a) \in R$ for $a, b \in T$;
- a relation $R$ on $T$ is antisymmetric if $(a, b),(b, a) \in R$ then $a=b$ for $a, b \in T$.

Let $\mathcal{S}$ and $\mathcal{A}$ be the set of all symmetric and antisymmetric relations on $T$ respectively. Then

• A

  $\mathcal{S} \cap \mathcal{A}=\emptyset$
• Correct answer
  B

  $|\mathcal{S} \cap \mathcal{A}|=2^n$
• C

  $|\mathcal{S}|=|\mathcal{A}|$
• D

  $\mathcal{S} \cup \mathcal{A}=T \times T$

Hence, the correct answer is option: 'B'.