1
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
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ (hungry(x) \vee threatened(x)) \to attacks(x)\} ]$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+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
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
A logical binary relation $$ \odot $$, is defined as follows: GATE CSE 2006 Discrete Mathematics - Mathematical Logic Question 33 English

Let ~ be the unary negation (NOT) operator, with higher precedence then $$ \odot $$. Which one of the following is equivalent to $$A \wedge B?$$

A
$$\left( { \sim A \odot B} \right)$$
B
$$\left( { \sim A \odot \sim B} \right)$$
C
$$ \sim \left( { \sim A \odot \sim B} \right)$$
D
$$ \sim \left( { \sim A \odot B} \right)$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the following first order logic formula in which $$R$$ is a binary relation symbol.
$$\forall x\forall y\left( {R\left( {x,\,y} \right) \Rightarrow R\left( {y,x} \right)} \right).$$

The formula is

A
Satisfiable and valid
B
Satisfiable and so is its negation
C
Unsatisfiable but its negation is valid
D
Satisfiable but its negation is unsatisfiable
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