The Boolean expression F = (x.y' + x'.y + x'.y') is equivalent to:
2022
The Boolean expression F = (x.y' + x'.y + x'.y') is equivalent to:
- A.
x + y'
- B.
x' + y'
- C.
x' + y
- D.
x + y
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Correct answer: B
Step 1: Start with the given Boolean expression: F = x.y' + x'.y + x'.y'.
Step 2: Factor out x' from the last two terms: x'.y + x'.y' = x'.(y + y').
Step 3: Since y + y' = 1, we get x'.(1) = x'. So the expression becomes: F = x.y' + x'.
Step 4: Now, use the Boolean identity: x' + x y' = (x' + x)(x' + y')
F = 1 · (x' + y')
F = x' + y'
Final Answer:
F = x' + y'