WB JEE 2020 | Sets and Relations Question 23 | Mathematics

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then

p is equivalence relation

p is reflexive and symmetric but is not transitive

p is reflexive and transitive but is not symmetric

p is reflexive only

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

Let p₁ and p₂ be two equivalence relations defined on a non-void set S. Then

both p₁ $$ \cap $$ p₂ and p₁ $$ \cup $$ p₂ are equivalence relations

$${p_1} \cap {p_2}$$ is equivalence relation but $${p_1} \cup {p_2}$$ is not so

$${p_1} \cup {p_2}$$ is equivalence relation but $${p_1} \cap {p_2}$$ is not so

neither $${p_1} \cap {p_2}$$ nor $${p_1} \cup {p_2}$$ is equivalence relation.

WB JEE 2019

MCQ (Single Correct Answer)

-0.25

Let the relation $$\rho $$ be defined on R as a$$\rho $$b if 1 + ab > 0. Then,

$$\rho $$ is reflexive only.

$$\rho $$ is equivalence relation.

$$\rho $$ is reflective and transitive but not symmetric.

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

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.

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

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

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