(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 Relations and Functions 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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Relations and Functions

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Types of Relations

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Let $R$ be a relation from $Q$ to $Q$ defined by $R = \{(a, b) : a, b \in Q \text{ and } a - b \in Z\}$. Show that $(a, b) \in R$ implies that $(b, a) \in R$.

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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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Let $L$ be the set of all straight lines in the Euclidean plane. Two lines $l_1$ and $l_2$ are related by the relation $R$ if and only if $l_1$ is parallel to $l_2$. Then the relation $R$ is:

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If $R$ is a relation from set $A$ to set $B$ and $S$ is a relation from set $B$ to set $C$,then the relation $S \circ R$ is:

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In the set of all $3 \times 3$ real matrices, a relation is defined as follows: $A$ matrix $A$ is related to a matrix $B$ if and only if there exists a non-singular $3 \times 3$ matrix $P$ such that $B = P^{-1} A P$. This relation is

MediumWBJEE 2013

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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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Let $R$ be a relation from $Q$ to $Q$ defined by $R = \{(a, b) : a, b \in Q \text{ and } a - b \in Z\}$. Show that $(a, b) \in R$ implies that $(b, a) \in R$.

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Let $L$ be the set of all straight lines in the Euclidean plane. Two lines $l_1$ and $l_2$ are related by the relation $R$ if and only if $l_1$ is parallel to $l_2$. Then the relation $R$ is:

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In the set of all $3 \times 3$ real matrices, a relation is defined as follows: $A$ matrix $A$ is related to a matrix $B$ if and only if there exists a non-singular $3 \times 3$ matrix $P$ such that $B = P^{-1} A P$. This relation is

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