1
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 $${\rm I}$$$${\rm I}$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let E, F and G be finite sets.
Let $$X = \,\left( {E\, \cap \,F\,} \right)\, - \,\left( {F\, \cap \,G\,} \right)$$
and $$Y = \,\left( {E\, - \left( {E\, \cap \,G} \right)} \right)\, - \,\left( {E\, - \,F\,} \right)$$. Which one of the following is true?
A
$$X\, \subset \,Y$$
B
$$X\, \supset \,Y$$
C
$$X\, = \,Y$$
D
$$X\, - \,Y\, \ne \,\emptyset \,\,and\,\,X\, - \,Y\, \ne \,\emptyset \,\,$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
A relation $$R$$ is defined on ordered pairs of integers as follows: $$\left( {x,y} \right)R\left( {u,v} \right)\,if\,x < u$$ and $$y > v$$. Then $$R$$ is
A
Neither a Partial Order nor an Equivalence Relation
B
A Partial Order but not a Total Order
C
A Total Order
D
An Equivalence relation
4
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
Let $$X,. Y, Z$$ be sets of sizes $$x, y$$ and $$z$$ respectively. Let $$W = X x Y$$ and $$E$$ be the set of all subjects of $$W$$. The number of functions from $$Z$$ to $$E$$ is
A
$${2^{{2^{xy}}}}$$
B
$$2 \times {2^{xy}}$$
C
$${2^{{2^{x + y}}}}$$
D
$${2^{xyz}}$$
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