Let X be a set and 2X denote the powerset of X. Define a binary operation Δ on 2X as follows:
AΔB = (A − B) ∪ (B − A)
Let H = (2X, Δ).
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 ∈ 2X, the inverse of A is the complement of A.
(D)
For every A ∈ 2X, the inverse of A is A.
Answer
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