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# Discrete mathematics

## Show that union of equivalence relation is always a equivalence relation.

Proof: Let, R1 and R2 be two equivalence relation For all a∊ A, (a, a) ∊ R1 and (a, a) ∊ R2. Since R1 and R2 are reflexive. ∴ (a, a) ∊ R1 ∪ R2 So R1 ∪ R2 is reflexive. If (a, b) ∊ R1 ∪ R2, then (a, ...

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## Relation

Relation Binary relation: A binary relation from A to B is a subset of A×B. A binary relation is indeed only a formalization of the initiative notion that some of the elements in A related to the some of the elements in B. If R is a binary relation from ...

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## Proposition

Proposition Definition: A proposition is a declarative sentence that is either true or false. Example: 1. It rained yesterday. 2. Dhaka is the capital of Bangladesh. A sense which has no true or false answer or value is not proposition. Example: 1. What time is it? 2. Where are you ...

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## Trees-brance node-terminal node-edge-vertex

Definition: A tree to be a connected group that contains no simple circuit. A collection of disjoint trees is called a forest. A vertex of degree 1 in a tree is called a half or terminal node and a vertex of degree larger than 1 is called a branch node ...

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