Consider the following boolean equations: (i) wx + w(x + y) + x(x + y) = x +…
2018
Consider the following boolean equations:
(i) wx + w(x + y) + x(x + y) = x + wy
(ii) (wx′(y + xz′) + w′x′)y = x′y
What can you say about the above equations ?
- A.
Both (i) and (ii) are true
- B.
(i) is true and (ii) is false
- C.
Both (i) and (ii) are false
- D.
(i) is false and (ii) is true
Attempted by 77 students.
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Correct answer: A
Solution summary: both expressions simplify to x' y (overline{x} y).
Start with the expression inside parentheses: w x' (y + x z') + w' x'. Factor x': x' [ w (y + x z') + w' ].
Use the identity w' + w*A = w' + A to simplify the bracket: w (y + x z') + w' = w' + y + x z'.
Now multiply by y (the outer factor): x' * y * (w' + y + x z') = x' * y, because y absorbs the sum (y*(w' + y + x z') = y).
Therefore each given equation equals x' y (overline{x} y). Since both written expressions are the same and simplify to x' y, both equations are true.
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