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The minimal expression of A + A'BA is

  • A.A
  • B.A + B
  • C.AB
  • D.B

Answer: A

The minimal expression is A.

The second term contains both A and its complement, which makes it 0:

\[ \begin{aligned} A + A'BA &= A + (A'A)B \\ &= A + 0 \cdot B \\ &= A + 0 = A \end{aligned} \]

A + B would be the answer to the different expression A + A'B, which is the likely trap. AB and B do not follow, since the term A'BA contributes nothing for any input. A quick check: if A = 1 the expression is 1, and if A = 0 every term contains A or is A, so it is 0; the output always equals A.

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