Define equivalence relation. How do you represent relation? | Discrete Structure 2080.1

Discrete Structure2080.15 marksEquivalence relations

Define equivalence relation. How do you represent relation? [5]

A relation R on a set A is called an equivalence relation if it satisfies the following three properties simultaneously: For every element $a \in A$ : $a \mathrel{R} a$ Every element is related to itself. For all $a, b \in A$ : $a \mathrel{R} b \implies b \mathrel{R} a$ For all $a, b, c \in A$ :...

A relation R on a set A is called an equivalence relation if it satisfies the following three properties simultaneously: For every element $a \in A$: $$a \mathrel{R} a$$ Every element is related to itself. For all $a, b \in A$: $$a \mathrel{R} b \implies b \mathrel{R} a$$ For all $a, b, c \in A$:...

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