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
Let $$P, Q$$, and $$R$$ be sets. Let $$\Delta $$ denote the symmetric difference operator defined as $$P\Delta Q = \left( {P \cup Q} \right) - \left( {P \cap Q} \right)$$. Using venn diagrams, determine which of the following is/are TRUE.

($${\rm I}$$) $$P\Delta \left( {Q \cap R} \right) = \left( {P\Delta Q} \right) \cap \left( {P\Delta R} \right)$$
($${\rm I}{\rm I}$$) $$P \cap \left( {Q\Delta R} \right) = \left( {P \cap Q} \right)\Delta \left( {P \cap R} \right)$$

A
$${\rm I}$$ only
B
$${\rm I}$$$${\rm I}$$ only
C
Neither $${\rm I}$$ nor $${\rm I}$$$${\rm I}$$
D
Both $${\rm I}$$ and $${\rm I}$$$${\rm I}$$
3
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
4
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 37 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
$$ \sim \left( { \sim A \odot B} \right)$$
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