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Tag Archives: math

A tree has two vertices of degree 2. One vertex of degree 3 and 3 vertices of degree 4.How many vertices of degree 1 does it have?

Exercise:A tree has 2n vertices of degree 1. 3n vertices of degree 2 and n vertices of degree 3. Determine the number of vertices and edges in the tree. Solution: 2n vertices has total degree = 2n× 1 = 2n 3n       ″      ″    ″      ″   = 3n×2 =6n n       ″     ...

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Prove that if two chords of a circle bisect each other, their point of intersection is the centre of the circle.

General enunciation: If two chords of a circle bisect each other, we have to show that their point of intersection is the centre of the circle. Particular enunciation: Suppose two chords AC and BD of the circle ABCD bisect each other at the point O i.e., OA = OC and ...

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Absorption Property, Idempotent Property| Discrete mathematics

Absorption Property: For any a, b in A, a˅(a˄b) =a and a˄(a˅b)=a Proof: Since a˅(a˄b) is the join of a and (a˄b) then , a˅(a˄b) ≥a ————————-(1) Since a≥a and a≥(a˄b) which implies that   (a˅a) ≥ a˅(a˄b) ⇒ a≥ a˅(a˄b) ———————————(2) From (1) and (2) we get, a˅(a˄b)=a Now ...

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Prove that the line segment joining the middle point of the hypotenuse of a right angle triangle and the opposite vertex is half the hypotenuse.

General enunciation: We have to prove that the line segment joining the middle point of the hypotenuse of a right angle triangle and the opposite vertex is half the hypotenuse. Particular enunciation: Suppose in right angle triangle ∆ABC, ∠B=900 and AC is hypotenuse. BO is the line joining the middle ...

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