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

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1.Relation and Function

normal

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

For any $a \in R$ , we have $a \geq a$, 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 $a \geq b$ and $b \geq c$ which is turn imply that $a \geq c$ .

Standard 12

Mathematics

Let $R$ be a relation on $N$ defined by $x + 2y = 8$. The domain of $R$ is

easy

Let the relations $R_1$ and $R_2$ on the set $\mathrm{X}=\{1,2,3, \ldots, 20\}$ be given by $\mathrm{R}_1=\{(\mathrm{x}, \mathrm{y}): 2 \mathrm{x}-3 \mathrm{y}=2\}$ and $\mathrm{R}_2=\{(\mathrm{x}, \mathrm{y}):-5 \mathrm{x}+4 \mathrm{y}=0\}$. If $\mathrm{M}$ and $\mathrm{N}$ be the minimum number of elements required to be added in $R_1$ and $R_2$, respectively, in order to make the relations symmetric, then $\mathrm{M}+\mathrm{N}$ equals

hard

(JEE MAIN-2024)

Maximum number of equivalence relations on set $A = \{1, 2, 3, 4\}$ is $N$, then –

normal

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false

normal

Let $S=\{1,2,3, \ldots, 10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R=\{(A, B): A \cap B \neq \phi ; A, B \in M\}$ is :

hard

(JEE MAIN-2024)

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

Solution

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Let $R$ be a relation on $N$ defined by $x + 2y = 8$. The domain of $R$ is

Maximum number of equivalence relations on set $A = \{1, 2, 3, 4\}$ is $N$, then –

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false

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