1
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
2
GATE CSE 2006
+2
-0.6
A logical binary relation $$\odot$$, is defined as follows: 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
$$\sim \left( { \sim A \odot B} \right)$$
3
GATE CSE 2006
+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
+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 $${\rm I}$$$${\rm I}$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
EXAM MAP
Joint Entrance Examination