(B) $1$. Reflexive: $A$ relation $R$ is reflexive if $(a, a) \in R$ for all $a \in \mathbb{R}$. Here,$a < a$ is false for any real number $a$. Thus,$R

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transitive but not reflexive and symmetric.

(B) $1$. Reflexive: $A$ relation $R$ is reflexive if $(a, a) \in R$ for all $a \in \mathbb{R}$. Here,$a $2$. Symmetric: $A$ relation $R$ is symmetric if $(a, b) \in R \implies (b, a) \in R$. If $a $3$. Transitive: $A$ relation $R$ is transitive if $(a, b) \in R$ and $(b, c) \in R \implies (a, c) \in R$. If $a Therefore,$R$ is transitive but not reflexive and symmetric.

Class 12 Mathematics Relation and Function Types of Relations

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Relation $R = \{(a, b): a < b\}$ is defined on the set of real numbers. Then $R$ is . . . . . . .

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A
reflexive and transitive but not symmetric.
B
transitive but not reflexive and symmetric.
C
reflexive and symmetric but not transitive.
D
symmetric but not reflexive and transitive.

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Types of Relations

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Among the relations $S = \{(a, b) : a, b \in R - \{0\}, 2 + \frac{a}{b} > 0\}$ and $T = \{(a, b) : a, b \in R, a^2 - b^2 \in Z\}$,which of the following is true?

DifficultJEE MAIN 2023

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Let $A = \{1, 2, 3, 4\}$ and let $R = \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then $R$ is

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Let $R = \{(x, y) \in N \times N : \log_e(x + y) \leq 2\}$. Then the minimum number of elements, required to be added in $R$ to make it a transitive relation, is . . . . . . .

JEE MAIN 2026

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Let $A = \{2, 4, 6, 8\}$. $A$ relation $R$ on $A$ is defined by $R = \{(2, 4), (4, 2), (4, 6), (6, 4)\}$. Then $R$ is:

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In $\mathbb{R}$, a relation $p$ is defined as follows: $\forall a, b \in \mathbb{R}$, $a \ p \ b$ holds if $a^2-4ab+3b^2=0$. Then:

EasyWBJEE 2024

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Relation $R = \{(a, b): a < b\}$ is defined on the set of real numbers. Then $R$ is . . . . . . .

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Among the relations $S = \{(a, b) : a, b \in R - \{0\}, 2 + \frac{a}{b} > 0\}$ and $T = \{(a, b) : a, b \in R, a^2 - b^2 \in Z\}$,which of the following is true?

Let $A = \{1, 2, 3, 4\}$ and let $R = \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then $R$ is

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