Let {R₁} be a relation defined by {R₁} = { (a,,b)|a ge b,,a,,b ∈ R} . Then {R₁} is

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1.Relation and Function

medium

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a,\,b)|a \ge b,\,a,\,b \in R\} $. Then ${R_1}$ is

An equivalence relation on $R$

Reflexive, transitive but not symmetric

Symmetric, Transitive but not reflexive

Neither transitive not reflexive but symmetric

Solution

(b) For any $a \in R$, we have $a \ge a,$ Therefore the relation $R$ is reflexive but it is not symmetric as $(2, 1)$ $ \in R$ but $(1, 2)$ $ \notin R$. The relation $R$ is transitive also, because $(a,b) \in R,(b,c) \in R$ imply that $a \ge b$ and $b \ge c$ which is turn imply that $a \ge c$.

Standard 12

Mathematics

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is

normal

Let $R$ be a relation on a set $A$ such that $R = {R^{ – 1}}$, then $R$ is

easy

The number of relations $R$ from an $m$-element set $A$ to an $n$-element set $B$ satisfying the condition$\left(a, b_1\right) \in R,\left(a, b_2\right) \in R \Rightarrow b_1=b_2$ for $a \in A, b_1, b_2 \in B$ is

normal

(KVPY-2009)

Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm $$\Leftrightarrow$ $n$ is a factor of $m$ (i.e.,$ n|m$). Then $R$ is

medium

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x$ is wife of $y\}$

medium

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a,\,b)|a \ge b,\,a,\,b \in R\} $. Then ${R_1}$ is

Solution

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Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x$ is wife of $y\}$