1
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
$$P.\overline R + Q$$
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
Let fsa and $$pda$$ be two predicates such that fsa$$(x)$$ means $$x$$ is a finite state automation, and pda$$(y)$$ means that $$y$$ is a pushdown automation. Let $$equivalent$$ be another predicate such that $$equivalent$$$$(a,b)$$ means $$a$$ and $$b$$ are equivalent. Which of the following first order logic statements represents the following:

Each finite state automation has an equivalent pushdown automation.

A
$$\left( {\forall x\,\,fsa\left( x \right)} \right) \Rightarrow \left( {\exists y\,\,pda\left( y \right) \wedge \,equivalent\,\,\left( {x,\,y} \right)} \right)$$
B
$$ \sim \forall y\left( {\exists x\,\,fsa\left( x \right) \Rightarrow pda\left( y \right) \wedge \,equivalent\left( {x,\,y} \right)} \right)$$
C
$$\forall x\,\exists y\left( {fsa\left( x \right) \wedge pda\left( y \right) \wedge \,equivalent\left( {x,\,y} \right)} \right)$$
D
$$\forall x\,\exists y\left( {fsa\left( y \right) \wedge pda\left( x \right) \wedge \,equivalent\left( {x,\,y} \right)} \right)$$
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
$$P$$ 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 $${\rm I}$$$$V$$
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
CBSE
Class 12