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2) What is the simplest Boolean expression equivalent to A’B’C + ABC’?A) A’CB) A’ + CC) A’C’D) AC

Question

What is the simplest Boolean expression equivalent to

A'B'C + ABC'?

A) A'C
B) A' + C
C) A'C'
D) AC

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Solution

The simplest Boolean expression equivalent to A’B’C + ABC’ is A) A’C.

Here's the step by step solution:

  1. Given expression is A’B’C + ABC’.

  2. Apply the Consensus theorem which states that (A + B)(A' + C)(B + C) = (A + B)(A' + C).

  3. In this case, A = A', B = B', and C = C. So, the expression becomes A'C + BC'.

  4. But B and B' can't be true at the same time, so the term BC' is always false and can be removed.

  5. Therefore, the simplest Boolean expression equivalent to A’B’C + ABC’ is A'C.

So, the answer is A) A’C.

This problem has been solved

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