Let $X = A B C + B C A + C A B .$ . Evaluate X for
(a) A = 1, B = 0, C = 1,
(b) A = B = C = 1, and
(c) A = B = C = 0.

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Solution

Given:
Output $X = A B C + B C A + C A B$

(a) A = 1, B = 0, C = 1
$X = 1 . (\bar{0.1)} + 0 . (\bar{1.1)} + 1 . (\bar{1.0)} = 1 . \bar{0} + 0 . \bar{1} + 1 . \bar{0} = 1.1 + 0.0 + 1.1 = 1 + 0 + 1 = 1 + 1 = 1$

(b) A = B = C = 1
$X = 1 . (\bar{1.1)} + 1 . (\bar{1.1)} + 1 . (\bar{1.1)} = 1 . \bar{1} + 1 . \bar{1} + 1 . \bar{1} = 1.0 + 1.0 + 1.0 = 0 + 0 + 0 = 0$

(c) A = B = C = 0
$X = 0 . (\bar{0.0)} + 0 (\bar{0.0)} + 0 . (\bar{0.0)} = 0 . \bar{0} + 0 . \bar{0} + 0 . \bar{0} = 0.1 + 0.1 + 0.1 = 0 + 0 + 0 = 0$

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