Question Detail
Question
Let \( A, B, C \subseteq U \). Simplify \( (A \cap B) \cup (A \cap B^c) \)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
By the distributive law: (A ∩ B) ∪ (A ∩ B^c) = A ∩ (B ∪ B^c) = A ∩ U = A. However, A is not an option. The given options are only φ and A ∪ B. If the expression was (A ∩ B) ∪ (A^c ∩ B^c), that simplifies to complement. Here, it simplifies to A. Since A is not listed, perhaps the options are incomplete. Option A is φ, which is not correct. There must be a missing option or a misprint.
Hint
Use distributive law: (A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C).