The Boolean expression A+BC equals

To determine which expression is equivalent to A + BC, we simplify each option using Boolean algebra rules. Option 0: (A′+B)(A′+C) Step 1: Expand using distributive law: (A′+B)(A′+C) = A′A′ + A′C + A′B + BC. Step 2: Simplify: A′A′ = A′, so expression becomes A′ + A′C + A′B + BC. Step 3: A′ + A′C = A′ and A′ + A′B = A′, so final expression is A′ + BC. This is not equal to A + BC, so Option 0 is incorrect. Option 1: (A+B)(A+C) Step 1: Expand: (A+B)(A+C) = AA + AC + AB + BC. Step 2: Simplify: AA = A, so expression becomes A + AC + AB + BC. Step 3: A + AC = A and A + AB = A, so final expression is A + BC. This matches the given expression, so Option 1 is correct. Option 2: (A+B)(A+C)′ Step 1: Apply De Morgan's law: (A+C)′ = A′C′, so expression becomes (A+B)(A′C′). Step 2: Expand: (A+B)(A′C′) = AA′C′ + BA′C′. Step 3: AA′ = 0, so expression becomes 0 + BA′C′ = BA′C′. This is not equal to A + BC, so Option 2 is incorrect. Option 3: More than one of the above Since only Option 1 is correct, this option is incorrect. Option 4: None of the above Since Option 1 is correct, this option is incorrect.