1
WB JEE 2019
+2
-0.5
Let f : X $$\to$$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)
A
$${f^{ - 1}}(A) - {f^{ - 1}}(B) \supset {f^{ - 1}}(A - B)$$ but the opposite does not hold.
B
$${f^{ - 1}}(A) - {f^{ - 1}}(B) \subset {f^{ - 1}}(A - B)$$ but the opposite does not hold.
C
$${f^{ - 1}}(A - B) = {f^{ - 1}}(A) - {f^{ - 1}}(B)$$
D
$${f^{ - 1}}(A - B) = {f^{ - 1}}(A) \cup {f^{ - 1}}(B)$$
2
WB JEE 2019
+2
-0.5
Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U be so that gof : s $$\to$$ U is surjective. Then,
A
g and f are both surjective
B
g is surjective, f may not be so
C
f is surjective, g may not be so
D
f and g both may not be surjective
3
WB JEE 2018
+1
-0.25
On R, a relation $$\rho$$ is defined by x$$\rho$$y if and only if x $$-$$ y is zero or irrational. Then,
A
$$\rho$$ is equivalence relation
B
$$\rho$$ is reflexive but neither symmetric nor transitive
C
$$\rho$$ is reflexive and symmetric but not transitive
D
$$\rho$$ is symmetric and transitive but not reflexive
4
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.
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