Question

show that the relation R defined on the set A={1, 2} as R={(1, 1), (2, 2), (1, 2) } is not symmetric​

Answer 1

$\textbf{Given:}$

$\text{In set A=\{1,2\} , relation R=\{(1, 1),(2, 2),(1, 2)\} }$

$\textbf{To show:}$

$\text{R is not symmetric}$

$\textbf{Solution:}$

$\text{We know that,}$

A relation R defined on a set S is called symmetric if

$\text{for all (a,b){\in}S\;\implies\,(b,a){\in}S }$

$\text{Consider,}\;R=\{(1, 1),(2, 2),(1, 2)\}$

$(1,2){\in}R$

$\text{But,}\;(2,1){\notin}R$

$\textbf{Hence, R is not symmetric}$

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R be a relation on Z defined by R= {(a,b): a-b is an integer} show that R is an equivalence relation

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