Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.
S1: (P # Q) # R = P # (Q # R) S2: Q # R = R # Q
Which of the following is/are true for the Boolean variables P, Q and R?
(A) Only S1 is True
(B) Only S2 is True
(C) Both S1 and S2 are True
(D) Neither S1 nor S2 are True
S2 is true, as X' + Y' = Y' + X'
S1 is false.
Let P = 1, Q = 1, R = 0, we get different results
(P # Q) # R = (P' + Q')' + R' = (0 + 0)' + 1 = 1 + 1 = 1
P # (Q # R) = P' + (Q' + R')' = 0 + (0 + 1)' = 0 + 0 = 0
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