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Excercise 1B

Let $R=\{(a, b): a, b \in Z$ and $(a-b)$ is divisible by 5 $\}$ Show that $\mathrm{R}$ is an equivalence relation on $\mathrm{Z}$ .

CBSE, Class 12, Excercise 1B, Maths, Relations, RS Aggarwal

Solution: $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathrm{Z}$ and $(\mathrm{a}-\mathrm{b})$ is divisible by 5$\}$ (As given) If $R$ is Reflexive, Symmetric and Transitive,...

Let $R=\{(a, b): a, b \in Z$ and $(a+b)$ is even $\}$ . Show that $R$ is an equivalence relation on $Z$ .

CBSE, Class 12, Excercise 1B, Maths, Relations, RS Aggarwal

Solution: $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathrm{Z}$ and $(\mathrm{a}+\mathrm{b})$ is even $\}$ (As given) If $R$ is Reflexive, Symmetric and Transitive, then $R$...

Define a relation on a set. What do you mean by the domain and range of a relation? Give an example.

CBSE, Class 12, Excercise 1B, Maths, Relations, RS Aggarwal

Solution: Relation: Suppose $P$ and $Q$ are two sets. Therefore, a relation $R$ from $P$ to $Q$ is a subset of $P \times Q$. Therefore, $\mathrm{R}$ is a relation to $\mathrm{P}$ to $\mathrm{Q}...

Let $R=\{(a, b): a, b \in Z$ and $(a-b)$ is divisible by 5 $\}$ Show that $\mathrm{R}$ is an equivalence relation on $\mathrm{Z}$ .

Let $R=\{(a, b): a, b \in Z$ and $(a+b)$ is even $\}$ . Show that $R$ is an equivalence relation on $Z$ .

Define a relation on a set. What do you mean by the domain and range of a relation? Give an example.

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Let and is divisible by 5 Show that is an equivalence relation on .

Let and is even . Show that is an equivalence relation on .

Define a relation on a set. What do you mean by the domain and range of a relation? Give an example.

Let $R=\{(a, b): a, b \in Z$ and $(a-b)$ is divisible by 5 $\}$ Show that $\mathrm{R}$ is an equivalence relation on $\mathrm{Z}$ .

Let $R=\{(a, b): a, b \in Z$ and $(a+b)$ is even $\}$ . Show that $R$ is an equivalence relation on $Z$ .