CBSE Class 12 Mathematics Relations and Functions Q #2170
KNOWLEDGE BASED
REMEMBER
5 Marks Generic-Curriculum LA
Check whether the relation $R$ in the set $N$ of natural numbers given by $R = \{(a, b) : a \text{ is divisor of } b\}$ is reflexive, symmetric or transitive. Also determine whether $R$ is an equivalence relation. [Delhi 2020]
Prev Next

More from this Chapter

SA
Let $A = \{1, 2, 3\}$. Then, find the number of relations containing $(1, 2)$ and $(1, 3)$, which are reflexive and symmetric but not transitive.
SA
Show that the relation $R$ in the set $R$ of real numbers, defined as $R = \{(a, b) : a \le b^2\}$ is neither reflexive nor symmetric nor transitive. [All India 2024]
VSA
Check whether $f:Z\times Z \rightarrow Z\times Z$ (where Z is the set of integers) defined as $f(x,y)=(2y,3x)$ is injective or not.
SA
A student wants to pair up natural numbers in such a way that they satisfy the equation $2x+y=41$, $x, y\in N$. Find the domain and range of the relation. Check if the relation thus formed is reflexive, symmetric and transitive. Hence, state whether it is an equivalence relation or not.
LA
Let $f : \mathbb{R} - \left\{ \frac{4}{3} \right\} \to \mathbb{R}$ be a function defined as:$$f(x) = \frac{4x}{3x+4}$$Show that $f$ is a one-one function. Also, check whether $f$ is an onto function or not.
View All Questions