1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $R$ be the set of real numbers.

Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$.

Statement II : $ B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$.
A
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B
Statement I is true, Statement II is false.
C
Statement I is false, Statement II is true.
D
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Consider the following relations

$R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$;

$S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.$ and $q$ are integers such that $n, q \neq 0$ and $q m=p m\}$. Then
A
$R$ is an equivalence relation but $S$ is not an equivalence relation
B
Neither $R$ nor $S$ is an equivalence relation
C
$S$ is an equivalence relation but $R$ is not an equivalence relation
D
$R$ and $S$ both are equivalence relations
3
AIEEE 2009
MCQ (Single Correct Answer)
+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
$A=B$
4
AIEEE 2008
MCQ (Single Correct Answer)
+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
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