GATE | GATE-CS-2000 | Question 33
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.
Â
Statement 1 :Â 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.
Â
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.
Â
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.
Â
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.
Quiz of this Question
Last Updated :
19 Nov, 2018
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...