WB JEE 2019 | Sets and Relations Question 26 | Mathematics

WB JEE 2019

MCQ (Single Correct Answer)

-0.5

Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)

$${f^{ - 1}}(A) - {f^{ - 1}}(B) \supset {f^{ - 1}}(A - B)$$ but the opposite does not hold.

$${f^{ - 1}}(A) - {f^{ - 1}}(B) \subset {f^{ - 1}}(A - B)$$ but the opposite does not hold.

$${f^{ - 1}}(A - B) = {f^{ - 1}}(A) - {f^{ - 1}}(B)$$

$${f^{ - 1}}(A - B) = {f^{ - 1}}(A) \cup {f^{ - 1}}(B)$$

WB JEE 2019

MCQ (Single Correct Answer)

-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,

g and f are both surjective

g is surjective, f may not be so

f is surjective, g may not be so

f and g both may not be surjective

WB JEE 2018

MCQ (Single Correct Answer)

-0.25

On R, a relation $$\rho $$ is defined by x$$\rho $$y if and only if x $$-$$ y is zero or irrational. Then,

$$\rho $$ is equivalence relation

$$\rho $$ is reflexive but neither symmetric nor transitive

$$\rho $$ is reflexive and symmetric but not transitive

$$\rho $$ is symmetric and transitive but not reflexive

WB JEE 2018

MCQ (Single Correct Answer)

-0.25

On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.

If | x $$-$$ y | < 2, then $$\rho $$ is reflexive but neither symmetric nor transitive.

If x $$-$$ y < 2, then $$\rho $$ is reflexive and symmetric but not transitive.

If | x | $$ \ge $$ y, then $$\rho $$ is reflexive and transitive but not symmetric

If x > | y |, then $$\rho $$ is transitive but neither reflexive nor symmetric.

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