1
GATE CSE 2008
+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
$$\left[ {\exists x,\alpha \wedge \left( {\forall y,\beta \wedge \left( {\exists u,\forall v,\neg \gamma } \right)} \right)} \right]$$
2
GATE CSE 2007
+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
$$\forall x\exists yP\left( {x,y} \right) \Rightarrow \exists y\forall xP\left( {x,y} \right)$$
3
GATE CSE 2006
+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
$$\forall x[(tiger(x) \vee lion(x)) \to$$$$\{ (hungry(x) \vee threatened(x)) \to attacks(x)\} ]$$
4
GATE CSE 2006
+2
-0.6
Consider the following propositional statements:

$${\rm P}1:\,\,\left( {\left( {A \wedge B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \wedge \left( {B \to C} \right)} \right)$$
$${\rm P}2:\,\,\left( {\left( {A \vee B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \vee \left( {B \to C} \right)} \right)$$ Which one of the following is true?

A
$$P1$$ is tautology, but not $$P2$$
B
$$P2$$ is tautology, but not $$P1$$
C
$$P1$$ and $$P2$$ are both tautologies
D
Both $$P1$$ and $$P2$$ are not tautologies
GATE CSE Subjects
EXAM MAP
Medical
NEET