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’CB) A’ + CC) A’C’D) AC
Solution
The simplest Boolean expression equivalent to A’B’C + ABC’ is A) A’C.
Here's the step by step solution:
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Given expression is A’B’C + ABC’.
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Apply the Consensus theorem which states that (A + B)(A' + C)(B + C) = (A + B)(A' + C).
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In this case, A = A', B = B', and C = C. So, the expression becomes A'C + BC'.
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But B and B' can't be true at the same time, so the term BC' is always false and can be removed.
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Therefore, the simplest Boolean expression equivalent to A’B’C + ABC’ is A'C.
So, the answer is A) A’C.
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