CBSE Class 12 Mathematics Relations and Functions Q #2177
KNOWLEDGE BASED
REMEMBER
5 Marks Generic-Curriculum LA
Show that the relation $R$ in the set $A = \{1, 2, 3, 4, 5\}$ given by $R = \{(a, b) \in A : |a - b| \text{ is even}\}$, is an equivalence relation. Show that all the elements of $\{1, 3, 5\}$ are related to each other and all the elements of $\{2, 4\}$ are related to each other, but no element of $\{1, 3, 5\}$ is related to any element of $\{2, 4\}$.
Prev Next

More from this Chapter

SA
Let $n$ be a fixed positive integer. Define a relation $R$ in $Z$ as follows $\forall a, b \in Z$, $a R b$ if and only if $a - b$ is divisible by $n$. Show that $R$ is an equivalence relation.
LA
A relation R is defined on $N\times N$ (where N is the set of natural numbers) as: $(a, b)~R~(c,d)\Leftrightarrow a-c=b-d$ Show that R is an equivalence relation.
LA
Prove that the function $f : N \to N$, defined by $f(x) = x^2 + x + 1$ is one-one but not onto. [Delhi 2019]
LA
Let $L$ be the set of all lines in $XY$ plane and $R$ be the relation in $L$ defined as $R = \{(L_1, L_2) : L_1 \text{ is parallel to } L_2\}$. Show that $R$ is an equivalence relation. Find the set of all lines related to the line $y = 2x + 4$. [NCERT]
VSA
A relation $R$ in set $A = \{1, 2, 3\}$ is defined as $R = \{(1, 1), (1, 2), (2, 2), (3, 3)\}$. Find ordered pair in $R$ shall be removed to make it an equivalence relation in $A$.
View All Questions