LA

Show that the relation $R$ defined in the set $A$ of all polygons as $R = \{(P_1, P_2) : P_1 \text{ and } P_2 \text{ have same number of sides}\}$, is an equivalence relation. What is the set of all elements in $A$ related to the right angled triangle $T$ with sides $3, 4$ and $5$?

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.

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 $A = \text{set of workers in a publication house}$. Let $a R b$, if and only if $a$ and $b$ tell lie ; $a, b \in A$. (i) Is $R$ symmetric relation? (ii) Is this relation an equivalence relation?

SA

Let $A = \text{a set of people}$. Let $a R b$ if and only if $a$ and $b$ are brothers. (i) Is the relation reflexive? (ii) Is the relation symmetric? (iii) Is the relation an equivalence relation?

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