Q41

MSQ2 marks

Let $X$ be a set and $2^{X}$ denote the powerset of $X$ . Define a binary operation $\Delta$ on $2^{X}$ as follows:

A \Delta B=(A-B) \cup(B-A) \text {. }

Let $H=\left(2^{X}, \Delta\right)$ . Which of the following statements about $H$ is/are correct?

(A)

$H$ is a group.

(B)

Every element in $H$ has an inverse, but $H$ is NOT a group.

(C)

For every $A \in 2^{X},$ the inverse of $A$ is the complement of $A$ .

(D)

For every $A \in 2^{X},$ the inverse of $A$ is $A$ .

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