1
WB JEE 2018
+1
-0.25
On the set R of real numbers, the relation $$\rho$$ is defined by x$$\rho$$y, (x, y) $$\in$$ R.
A
If | x $$-$$ y | < 2, then $$\rho$$ is reflexive but neither symmetric nor transitive.
B
If x $$-$$ y < 2, then $$\rho$$ is reflexive and symmetric but not transitive.
C
If | x | $$\ge$$ y, then $$\rho$$ is reflexive and transitive but not symmetric
D
If x > | y |, then $$\rho$$ is transitive but neither reflexive nor symmetric.
2
WB JEE 2018
+2
-0.5
Let $$\rho$$ be a relation defined on N, the set of natural numbers, as

$$\rho$$ = {(x, y) $$\in$$ N $$\times$$ N : 2x + y = 41}. Then
A
$$\rho$$ is an equivalence relzation.
B
$$\rho$$ is only reflexive relation
C
$$\rho$$ is only symmetric relation
D
$$\rho$$ is not transitive
3
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
4
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
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