WB JEE 2021 | Sets and Relations Question 23 | Mathematics

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

Let R be the real line. Let the relations S and T or R be defined by

$$S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y$$ is an integer}. Then

both S and T are equivalence relations on R

T is an equivalence on R but S is not

neither S nor T is an equivalence relation on R

S is an equivalence relation on R but T is not

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.

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