Boolean expression ~ (A * B) * (~A + B) * (~B + B) is equal to which of the…

Step 1: Simplify (~B + B) to 1, since any variable OR its complement is always true. Step 2: The expression becomes ~(A * B) * (~A + B) * 1. Step 3: Apply De Morgan's law: ~(A * B) = ~A + ~B. Step 4: The expression is now (~A + ~B) * (~A + B). Step 5: Distribute the terms: (~A + ~B) * (~A + B) = ~A * ~A + ~A * B + ~B * ~A + ~B * B. Step 6: Simplify each term: ~A * ~A = ~A, ~A * B = ~A * B, ~B * ~A = ~A * ~B, ~B * B = 0. Step 7: Combine terms: ~A + ~A * B + ~A * ~B + 0. Step 8: Factor out ~A: ~A * (1 + B + ~B) = ~A * 1 = ~A.