1
WB JEE 2017
+1
-0.25
On the set R of real numbers we define xPy if and only if xy $$\ge$$ 0. Then, the relation P is
A
reflexive but not symmetric
B
symmetric but not reflexive
C
transitive but not reflexive
D
reflexive and symmetric but not transitive
2
WB JEE 2017
+1
-0.25
On R, the relation $$\rho$$ be defined by 'x$$\rho$$y holds if and only if x $$-$$ y is zero or irrational'. Then,
A
$$\rho$$ is reflexive and transitive but not symmetric
B
$$\rho$$ is reflexive and symmetric but not transitive
C
$$\rho$$ is symmetric and transitive but not reflexive
D
$$\rho$$ is equivalence relation
3
WB JEE 2017
+2
-0.5
On set A = {1, 2, 3}, relations R and S are given by

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},

S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,
A
R $$\cup$$ S is an equivalence relation
B
R $$\cup$$ S is reflexive and transitive but not symmetric
C
R $$\cup$$ S is reflexive and symmetric but not transitive
D
R $$\cup$$ S is symmetric and transitive but not reflexive
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