The reduced form of the Boolean expression (A+B)(A+C) is: A. AB+AC B. A+B+C C. AC+B D. A+BC E. None of the above

The correct answer is A. AB+AC.

The Boolean expression (A+B)(A+C) can be expanded as follows:

(A+B)(A+C) = AA + AB + AC + BA + BB + BC

= A^2 + AB + AC + AB + B^2 + BC

= A^2 + 2AB + AC + B^2

= (A+B)^2 + AC

The term (A+B)^2 is a perfect square, so it can be simplified as A^2 + 2AB + B^2. The term AC is not a perfect square, so it remains unchanged. Therefore, the reduced form of the Boolean expression (A+B)(A+C) is AB+AC.

Here is a brief explanation of each option:

• Option A: AB+AC is the correct answer.
• Option B: A+B+C is not the reduced form of the Boolean expression (A+B)(A+C). The term A+B+C is not a perfect square, so it cannot be simplified.
• Option C: AC+B is not the reduced form of the Boolean expression (A+B)(A+C). The term AC+B is not a perfect square, so it cannot be simplified.
• Option D: A+BC is not the reduced form of the Boolean expression (A+B)(A+C). The term A+BC
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  is not a perfect square, so it cannot be simplified.
• Option E: None of the above is the correct answer.