1
AIEEE 2009
+4
-1
If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then :
A
$A=C$
B
$B=C$
C
$A \cap B=\phi$
D
$A=B$
2
AIEEE 2008
+4
-1
Let R be the real line. Consider the following subsets of the plane $$R \times R$$ :
$$S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}$$
$$T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}$$,

Which one of the following is true ?

A
Neither S nor T is an equivalence relation on R
B
Both S and T are equivalence relation on R
C
S is an equivalence relation on R but T is not
D
T is an equivalence relation on R but S is not
3
AIEEE 2006
+4
-1
Let $W$ denote the words in the English dictionary. Define the relation $R$ by

$R=\{(x, y) \in W \times W \mid$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is
A
reflexive, symmetric and not transitive
B
reflexive, symmetric and transitive
C
reflexive, not symmetric and transitive
D
not reflexive, symmetric and transitive
4
AIEEE 2005
+4
-1
Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12)$, $(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$. The relation is :
A
reflexive and symmetric only
B
an equivalence relation
C
reflexive only
D
reflexive and transitive only
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