Mathematics · Group Theory
Let X be a non-empty set and P(X) be the set of all subsets of X. On P(X), define two operations ∗ and Δ as follows: for A, B ∈ P(X), A ∗ B = A ∩ B and A Δ B = (A ∪ B) \ (A ∩ B). Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1P(X) is neither a group under ∗ nor under Δ
- 2P(X) is a group under Δ, but not under ∗✓
- 3P(X) is a group under ∗, but not under Δ
- 4P(X) is a group under ∗ as well as under Δ
Correct answer
P(X) is a group under Δ, but not under ∗
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