VSA

Let $f:A\rightarrow B$ be defined by $f(x)=\frac{x-2}{x-3}$ where $A=R-\{3\}$ and $B=R-\{1\}$. Discuss the bijectivity of the function.

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 a set of real numbers $\mathbb{R}$ as:$$R = \{(x, y) : x \cdot y \text{ is an irrational number}\}$$Check whether $R$ is reflexive, symmetric, and transitive 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.

VSA

Let $f : R \to R$ be defined as $f(x) = \frac{x^2 + 1}{2}$, then check whether $f$ is one-one or onto.

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