1
GATE CSE 2019
+1
-0.33
Which one of the following is NOT a valid identity?
A
(x ⊕ y) ⊕ z = x ⊕ (y ⊕ z)
B
(x + y) ⊕ z = x ⊕ (y + z)
C
x ⊕ y = x + y, if xy = 0
D
x ⊕ y = (xy + x'y')'
2
GATE CSE 2016 Set 2
+1
-0.3
Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},\,{x_3},\,{x_4}$$ are Boolean Variables, and $$\oplus$$ is the $$XOR$$ operator.

Which one of the following must always be TRUE?

A
$${x_1}{x_2}{x_3}{x_4} = 0$$
B
$${x_1}{x_3} + {x_2} = 0$$
C
$${\overline x _1} \oplus {\overline x _3} = {\overline x _2} \oplus {\overline x _4}$$
D
$${x_1} + {x_2} + {x_3} + {x_4} = 0$$
3
GATE CSE 2016 Set 1
+1
-0.3
Consider the Boolean operator $$\ne$$ with the following properties:
$$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \ne x = 0$$ and $$x \ne \overline x = 1.$$ Then $$x \ne y$$ is equivalent to
A
$$x\overline y + \overline x y$$
B
$$x\overline y + \overline x \overline y$$
C
$$\overline x y + xy$$
D
$$xy + \overline x \overline y$$
4
GATE CSE 2015 Set 3
+1
-0.3
Let $$\ne$$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$𝑋$$ and $$𝑌$$ are Boolean variables. Consider the following two statements. \eqalign{ & \left( {S1} \right)\,\,\,\,\,\,\,\left( {P \ne Q} \right) \ne R = P \ne \left( {Q \ne R} \right) \cr & \left( {S2} \right)\,\,\,\,\,\,\,Q \ne R = R \ne Q \cr}\$

Which of the following is/are true for the Boolean variables $$𝑃, 𝑄$$ and $$𝑅$$?

A
Only $$S1$$ is true
B
Only $$S2$$ is true
C
Both $$S1$$ and $$S2$$ are true
D
Neither $$S1$$ nor $$S2$$ are true
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