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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 2007
MCQ (Single Correct Answer)
+2
-0.6
Which one of these first-order logic formulae is valid?
A
$$\forall x\left( {P\left( x \right) \Rightarrow Q\left( x \right)} \right) \Rightarrow \left( {\left( {\forall xP\left( x \right)} \right) \Rightarrow \left( {\forall xQ\left( x \right)} \right)} \right)$$
B
$$\exists x\left( {P\left( x \right) \vee Q\left( x \right)} \right) \Rightarrow \left( {\left( {\exists xP\left( x \right)} \right) \Rightarrow \left( {\exists xQ\left( x \right)} \right)} \right)$$
C
$$\exists x\left( {P\left( x \right) \wedge Q\left( x \right)} \right) \Leftrightarrow \left( {\left( {\exists xP\left( x \right)} \right) \wedge \left( {\exists xQ\left( x \right)} \right)} \right)$$
D
$$\forall x\exists yP\left( {x,y} \right) \Rightarrow \exists y\forall xP\left( {x,y} \right)$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Which one of the first order predicate calculus statements given below correctly expresses the following English statement?

Tigers and lion attack if they are hungry of threatened.

A
$$\forall x[(tiger(x) \wedge lion(x)) \to $$$$\{ (hungry(x) \vee threatened(x)) \to attacks(x)\} ]$$
B
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ (hungry(x) \wedge threatened(x)) \to attacks(x)\} ]$$
C
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ attacks(x) \to (hungry(x)) \vee threatened(x))\} ]$$
D
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ (hungry(x) \vee threatened(x)) \to attacks(x)\} ]$$
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