Define the connective * for the Boolean variables X and Y as: X * Y = XY + X’ Y’. Let Z = X * Y.
Consider the following expressions P, Q and R.
P: X = Y⋆Z
Q: Y = X⋆Z
R: X⋆Y⋆Z=1
Which of the following is TRUE?
(A) Only P and Q are valid
(B) Only Q and R are valid.
(C) Only P and R are valid.
(D) All P, Q, R are valid.
Answer: (D)
Explanation: * is nothing but working as EX NOR here.Explanation:
P:
X= Y * Z
=(Y XOR Z)’
=YZ + Y’Z’
=Y(XY + X’Y’)+Y’(XY+X’Y’)’
=XY+Y’((Y XOR X)’)’
=XY+Y’(Y XOR X)
=XY+Y’(Y’X+X’Y)
=XY+Y’X
=X(Y+Y’)
=X
Q:
Y=X*Z
=(X XOR Z)’
=X(XY + X’Y’) + X’(XY + X’Y’)’
=XY+X’(X’Y+XY’)
=XY+X’Y
=Y
R:
X * Y *Z
WE HAVE SEEN FROM P Y*Z =X
SO X * X
SO ALL P,Q,R ARE CORRECT
ANS IS (D)
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