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.

LA

Show that $f:R\rightarrow R$ defined as $f(x)=\frac{x}{\sqrt{1+x^{2}}}$ is one-one but not onto.

SA

Let R be a relation defined on a set N of natural numbers such that $R=\{(x,y): xy \text{ is a square of a natural number, } x, y\in N\}$. Determine if the relation R is an equivalence relation.

VSA

A relation R on $A=\{1,2,3\}$ is defined as $R=\{(1,1),(3,3),(1,2)\}$. Is R a symmetric relation? Justify. Write the smallest relation set $R_{1}$ such that $R\cup R_{1}$ becomes an equivalence relation on the set {1, 2, 3}.

LA

Check whether the relation S in the set of real numbers R defined by $S=\{(a,b)$: where $a-b+\sqrt{2}$ is an irrational number is reflexive, symmetric or transitive.

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