GATE CS 2023 Question 54: Group Properties of Powerset with Symmetric Difference | Examprev

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Computer Sciences > GATE 2023 > Discrete Mathematics

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

D

For every A ∈ 2^X, the inverse of A is A.

Correct : a,d

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Related Topics

powerset symmetric difference group theory binary operation delta inverse element GATE Computer Sciences 2023 GATE CS 2023 Q54 algebraic structure

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