Skip to content
Related Articles
GATE | GATE-CS-2007 | Question 85
• Difficulty Level : Medium
• Last Updated : 19 Nov, 2018

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

NOT(X XOR X)=X’X’+XX
1
```

SO ALL P,Q,R ARE CORRECT

ANS IS (D)

Quiz of this Question

Attention reader! Don’t stop learning now. Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up