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1
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
$$P$$ and $$Q$$ are two propositions. Which of the following logical expressions are equivalent?

$${\rm I}.$$ $${\rm P}\, \vee \sim Q$$
$${\rm I}{\rm I}.$$ $$ \sim \left( { \sim {\rm P} \wedge Q} \right)$$
$${\rm I}{\rm I}{\rm I}.$$ $$\left( {{\rm P} \wedge Q} \right) \vee \left( {{\rm P} \wedge \sim Q} \right) \vee \left( { \sim {\rm P} \wedge \sim Q} \right)$$
$${\rm I}V.$$ $$\left( {{\rm P} \wedge Q} \right) \vee \left( {{\rm P} \wedge \sim Q} \right) \vee \left( { \sim {\rm P} \wedge Q} \right)$$

A
Only $${\rm I}$$ and $${\rm I}$$$${\rm I}$$
B
Only $${\rm I}$$, $${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$
C
Only $${\rm I}$$, $${\rm I}$$$${\rm I}$$ and $${\rm I}$$$$V$$
D
All of $${\rm I}$$, $${\rm I}$$$${\rm I}$$, $${\rm I}$$$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$$V$$
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
Which of the following is the negation of $$$\left[ {\forall x,\alpha \to \left( {\exists y,\beta \to \left( {\forall u,\exists v,\gamma } \right)} \right)} \right]?$$$
A
$$\left[ {\exists x,\alpha \to \left( {\forall y,\beta \to \left( {\exists u,\forall v,\gamma } \right)} \right)} \right]$$
B
$$\left[ {\exists x,\alpha \to \left( {\forall y,\beta \to \left( {\exists u,\forall v,\neg \gamma } \right)} \right)} \right]$$
C
$$\left[ {\forall x,\neg \alpha \to \left( {\exists y,\neg \beta \to \left( {\forall u,\exists v,\neg \gamma } \right)} \right)} \right]$$
D
$$\left[ {\exists x,\alpha \wedge \left( {\forall y,\beta \wedge \left( {\exists u,\forall v,\neg \gamma } \right)} \right)} \right]$$
3
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
Which of the following first order formulae is logically valid? Here $$\alpha \left( x \right)$$ is a first order formulae with $$x$$ as a free variable, and $$\beta $$ is a first order formula with no free variable.
A
$$\left[ {\beta \to \left( {\exists x,\alpha \left( x \right)} \right)} \right] \to \left[ {\forall x,\beta \to \alpha \left( x \right)} \right]$$
B
$$\left[ {\exists x,\beta \to \alpha \left( x \right)} \right] \to \left[ {\beta \to \left( {\forall x,\alpha \left( x \right)} \right)} \right]$$
C
$$\left[ {\left( {\exists x,\alpha \left( x \right)} \right) \to \beta } \right] \to \left[ {\forall x,\alpha \left( x \right) \to \beta } \right]$$
D
$$\left[ {\left( {\forall x,\alpha \left( x \right)} \right) \to \beta } \right] \to \left[ {\forall x,\alpha \left( x \right) \to \beta } \right]$$
4
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
If $$P$$, $$Q$$, $$R$$ are Boolean variables, then $$(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$$ simplifies to
A
$$P.\overline Q $$
B
$$P.\overline R $$
C
$$P.\overline Q + R$$
D
$$P.\overline R + Q$$
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Questions Asked from Marks 2
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Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
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Computer Networks
Software Engineering
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General Aptitude
Discrete Mathematics
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