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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
Question
In set $A=\{0,1,2,3,4,5\} R$ is equivalence relation where $R =\{(a, b):(a-b)$ is divisible by 2$\}$. Write equivalence class [0].
✓

Answer

Equivalence class [0] is set of those elements of A which is related to zero.
i.e.$
[0]=\{(a, 0) \in R: a \in A\}
$
Now, $(a, 0) \in R$
$\Rightarrow a-0$ is divisible by 2 and $a \in A$
$\Rightarrow$$
a=0,2,4
$
thus$
[0]=\{0,2,4\}
$

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