Function Relation (Discrete math) Let A=\{0,1,2\} and r=\{(0,0),(1,1),(2,2)\}

Globokim8 2021-08-22 Answered
Function Relation (Discrete math)
Let \(\displaystyle{A}={\left\lbrace{0},{1},{2}\right\rbrace}\) and \(\displaystyle{r}={\left\lbrace{\left({0},{0}\right)},{\left({1},{1}\right)},{\left({2},{2}\right)}\right\rbrace}\)
Show that r is an equivalence relation on A.

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Expert Answer

tabuordg
Answered 2021-08-23 Author has 16512 answers
Step 1
The relation is reflexive, since \(\displaystyle{\left({a},{a}\right)}\in{R}\), where \(\displaystyle{a}\in{A}\)
Also, since \(\displaystyle{a}={b}\) where \(\displaystyle{\left({a},{b}\right)}\in{R}\) therefore, the relation is symmetric.
Step 2
The relation is trivial transitive, as
\(\displaystyle{\left({a},{b}\right)}\in{R},{\left({b},{c}\right)}\in{R},\rightarrow{\left({a},{c}\right)}\in{R}\)
\(\displaystyle{a}={b}={c}\)
The relation is reflexive, symmetric and transitive.
therefore, r is an equivalence relation.
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