Question Detail

MTH 101 MTH 101 Past Questions Objective Question

Question

Which of the following is always true?
Options
A \(A \cap A = A\)
B \(A \cup A = U\)
C \(A \cap A = \varnothing\)
D \(A \cup A = A\)
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

A ∪ A = A is always true. A ∩ A = A is also true, but that's option A. Both A and D are true. However, option A is A ∩ A = A, which is correct. Option D is A ∪ A = A, also correct. The question says "always true", and both are true. Possibly only one is listed as correct. Option A is standard.

Hint

Recall basic set identities: idempotent laws.

Question Info