(a) Is this boolean equation valid or invalid for all possible values of x,y and z?...

Question

Question

(a) Is this boolean equation valid or invalid for all possible values of x,y and z?...

(a) Is this boolean equation valid or invalid for all possible values of x,y and z?

x XOR (y OR z) = (x XOR y) OR (x XOR z)

(b) Prove your answer, by using a truth table

engineering Computer-Science

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Answer 1

Answer #1

(a)No

When x =1, y=1 and z=0

x xor (y or z) = 1 xor (1) = 0

(x xor y) or (x xor z) = (1 xor 1) or (1 xor 0) = 0 or 1 = 1

So equation is invalid in this case.

(b)

x y z L R
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 1 1
1 0 0 1 1
1 0 1 0 1
1 1 0 0 1
1 1 1 0 0

*L=Left hand side
*R=Right hand side

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Answer 2

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