Simplify the boolean expression (A AND NOT B) OR (A AND B).

Simplify the boolean expression (A AND NOT B) OR (A AND B).

• A. A
• B. NOT A
• C. A AND NOT B
• D. A OR B

Answer: (A)

The expression has a common factor A in both terms, so you can factor it: (A ∧ ¬B) ∨ (A ∧ B) = A ∧ (¬B ∨ B). The inside (¬B ∨ B) is always true (a tautology), so it becomes 1. Then A ∧ 1 equals A. So the whole expression simplifies to A. This also matches the behavior: if A is false, the whole thing is false; if A is true, the inside is true, so the result is true, i.e., A.

The expression has a common factor A in both terms, so you can factor it: (A ∧ ¬B) ∨ (A ∧ B) = A ∧ (¬B ∨ B). The inside (¬B ∨ B) is always true (a tautology), so it becomes 1. Then A ∧ 1 equals A. So the whole expression simplifies to A. This also matches the behavior: if A is false, the whole thing is false; if A is true, the inside is true, so the result is true, i.e., A.