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Shah Alam

I am a student of mathematics department of Begum Rokeya University, Rangpur. I want to provide all kinds of solution of mathematics problems by this web site.

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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Let R be a reflexive relation on a set A. Show that R is an equivalence relation if and only if (a,b) and (a,c) in R implies that (b,c) ∊R.

Proof: First we say that R is an equivalence relation. We have (a,b)∊R and (a,c) ∊R ⟹(b,a) ∊R and (a,c) ∊R [∵ R is symmetric] ⟹(b,c) ∊R Conversely, we suppose that (b,c) ∊R Given that R is reflexive. Let (a,b) ∊R, then there exist x∊A such that (x,a) ∊R and ...

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