The boolean function A + BC is a reduced form of ____________

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BlackTom AI · Accepted Answer

The question asks which option is equivalent to the reduced form of the Boolean function A + BC.
Option a: A’B + AB’C. This expression mixes complemented and uncomplemented variables and, when simplified, does not yield A + BC. It represents a different minterm/cover and does not cover the same input combinations as A + BC.
Option b: AB + BC. Factoring B gives B(A + C). This is not equivalent to A + BC in general. For example, when A = 0, B = 1, C = 0, AB + BC = 0, while A + BC = 0 + 0 = 0, so this case matches, but consider A = 1, B = 0, C = 1: AB + BC = 0, whereas A + BC = 1 + 0 = 1. The two expressions differ on some inputs, so they are not equivalent.
Option c: (A + B)(A + C). This is a classic Boolean algebra identity: A + BC = (A + B)(A + C). Expanding (A + B)(A + C) gives A(A + C) + B(A + C) = A + AB + AC + BC, which simplifies to A + BC, since A absorbs AB and AC. Therefore, this option is equivalent to A + BC.
Option d: (A + C)B. This is B(A + C) = AB + BC, which, as shown in option b, does not equal A + BC in general. It represents a different function for certain input combinations, so it is not equivalent.
In summary, options a, b, and d do not produce the same truth table as A + BC, while option c matches the well-known identity A + BC = (A + B)(A + C).

FIT1047_S1_2025 Week 2 quiz (not assessed)

The boolean function A + BC is a reduced form of ____________

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