Question

Explain the following with example.

Answer 1

\(\large \color{black}{\begin{align} &\normalsize \text{A relation R in a set A is called }\hspace{.33em}\\~\\
&(i)\quad \bf{reflexive}, \normalsize \text{if}\ (a,a)\in R,\normalsize \text{for every}\ a\in A,\hspace{.33em}\\~\\
&(ii)\quad \bf{symmetric},\normalsize \text{if}\ (a_1,a_2)\in \normalsize \text{R implies that }\\~\\ &\ (a_2,a_1)\in R\ \text{for all}\ a_1,a_2 \in A,\hspace{.33em}\\~\\
&(ii)\quad \bf{transitive }, \normalsize \text{if}\ (a_1,a_2)\in R\ \normalsize \text{and} \ (a_2,a_3)\in R\\~\\
& \normalsize \text{implies that} \ (a_1,a_3)\in R,\text{for all}\ a_1,a_2,a_3\in A
\end{align}}\)

Answer 2

equality on the real numbers works

Answer 3

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