The simultaneous equations on the Boolean variables x, y, z and w,
have the following solution for x, y, z and w, respectively.
(A) 0 1 0 0
(B) 1 1 0 1
(C) 1 0 1 1
(D) 1 0 0 0
Answer: (C)
Explanation: We solve this question by putting in the options in the statements.
Statement 1 : x + y + z = 1
OPTION x y z w LHS LHS=1 -------------------------------------- A 0 1 0 0 1 Yes B 1 1 0 1 1 Yes C 1 0 1 1 1 Yes D 1 0 0 0 1 Yes
Till now, all the options are possible.
Statement 2 : x y = 0
OPTION x y z w LHS LHS=0 -------------------------------------- A 0 1 0 0 0 Yes B 1 1 0 1 1 No C 1 0 1 1 0 Yes D 1 0 0 0 0 Yes
Since LHS ≠ 0, B is not possible.
Statement 3 : x z + w = 1
OPTION x y z w LHS LHS=1 -------------------------------------- A 0 1 0 0 0 No C 1 0 1 1 1 Yes D 1 0 0 0 0 No
Since LHS ≠ 1, A and D are not possible.
Statement 4 : x y + z’ w’ = 0
OPTION x y z w LHS LHS=0 -------------------------------------- C 1 0 1 1 0 Yes
Thus, C is the correct option.
Please comment below if you find anything wrong in the above post.
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