Mathematical Proof

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Denoting, as usual, by (a, b) an ”open interval”, {x : a<x< b} and by [a, b] the corresponding ”closed interval”, {x : a≤x≤b} of real numbers, prove that sup(a, b)=sup[a, b]=b and inf(a,... more

Please help me answer the following question! I'm stuck!   Prove that cos6ß + sin6ß = 1/4 + 3/4cos2ß   I've tried simplifying out the LHS into (cos2ß)3 + (sin2ß)3, but I don't know what to do... more

a, b, c are positive integers such that a>b>c   N is the largest three digit number that has the digits a, b and c. K is the smallest three digit number that has the digits a, b and... more

Use direct proof or contrapositive proof or proof by contradiction

I stucked with this after step one where u prove by substituting 1 into the unknowns.Do kindly assist.

Statements line WXY m<WXY = 180° m<WXZ = 135° m<WXY = m<WXZ + m<ZXY 180° = 135° + m<ZXY 45° = m<ZXY m<ZXY = 45°   Reasons  Given Defintion of supplementary... more

Am I wrong in thinking that the 2's in the numerator and denominator should cancel each other out, leaving me with ⌈𝑛+1⌉= n + 1, and because n + 1 is an integer, that it's ceiling is simply n + 1?... more

Prove or disprove. For all n in rational, 1/n ≠ n - 1

Prove or disprove the statement  if n is not divisible by 3, then n 2 + 2 is divisible by 3

We need to prove the following using proof by induction. I don't want the actual answer if you can avoid it, I just can't figure out how to do it because when I do it how my notes read I am... more

Prove the following statements using the First Principle of Mathematical Induction:(a) If r ≠ 1, then1 + r + r2 + ... + rn = (1 − rn+1)/(1-r) for all n ∈ N. Why does the formula not work when r =... more

Proof by mathematical induction that for every integer h ≥ 0 there exists binary tree of height h with 2h leaves.