Let $A = \{1, 2, 3\}$. Then, the number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive, is

Match List - I with List - II.

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If $f\left(x+\dfrac{1}{x}\right) = x^2 + \dfrac{1}{x^2}$ then $f(x) =$

A. A relation $R$ on a set $A$ is called an equivalence relation, if it is reflexive, symmetric and transitive.

B. The function $f : R \to R$ defined by $f(x) = e^x$ is not one-one.

C. The one-one function is also known as injective function.

D. The onto function is also known as subjective function.

E. A function $f : X \to Y$ is said to be many-one, if two or more than two elements in set $X$ have the different image in set $Y$.

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A function $f: \mathbb{R} \rightarrow \{x \in \mathbb{R}: -1 < x < 1\}$ is defined as $f(x) = \frac{x}{1+|x|}$, then $f$ is:

Let R be a relation on the set of natural numbers N defined by nRm if n divides m. Then R is :

(A) Reflexive Relation

(B) Symmetric Relation

(C) Transitive Relation

(D) Identity Relation

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If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$, then $f$ is