GATE CSE 2013 | GATE CSE Year Wise Previous Years Questions

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GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

The smallest integer that can be represented by an $$8$$-bit number in $$2's$$ complement form is

$$-256$$

$$-128$$

$$-127$$

$$0$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which one of the following expressions does NOT represent exclusive NOR of $$x$$ and $$y?$$

$$xy+x'y'$$

$$x \otimes y'$$

$$x' \otimes y$$

$$x' \otimes y'$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.6

What is the logical translation of the following statement?
"None of my friends are perfect."

$$\exists x\left( {F\left( x \right) \wedge \neg P\left( x \right)} \right)$$

$$\exists x\left( {\neg F\left( x \right) \wedge P\left( x \right)} \right)$$

$$\exists x\left( {\neg F\left( x \right) \wedge \neg P\left( x \right)} \right)$$

$$\neg \exists x\left( {F\left( x \right) \wedge P\left( x \right)} \right)$$

GATE CSE 2013

MCQ (More than One Correct Answer)

-0.6

Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$

$$\forall x\left( {\exists z\left( {\neg \beta } \right) \to \forall y\left( \alpha \right)} \right)$$

$$\forall x\left( {\forall z\left( \beta \right) \to \exists y\left( {\neg \alpha } \right)} \right)$$

$$\forall x\left( {\forall y\left( \alpha \right) \to \exists z\left( {\neg \beta } \right)} \right)$$

$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$

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