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
EXAM MAP
Medical
NEET