Recent content by jeszo

In response to Ray Vickson: With 0 and 5n as the equivalence class for 0, wouldn't it still hold true that 0~0,5n~0 and 0~5n? Since, 2(5n)+3(0)=5(2n) and 2(0)+3(5n)=5(3n)?

Homework Statement ~ is a equivalence relation on integers defined as: a~b if and only if 2a+3b is divisible by 5 What is the equivalence class of 0 Homework Equations The Attempt at a Solution [0] = {0, 5n} n is an integer My reasoning for choosing 0 is that if a=0...

Thanks for your responses, I understand my mistake now :smile:

Homework Statement Prove that √x+y ≤ √x + √y for all x,y ≥ 0 Homework Equations The Attempt at a Solution square both sides: x + y ≤ x + 2√x√y + y subtracting x and y: 0 ≤ 2√x√y dividing by 2: 0 ≤ √x√y 0 ≤ √x√y is true for all x,y since the square root of a...

Homework Statement Relation on set of integers. a~b if and only if 2a+3b is divisible by 5 show that ~ is an equivalence relation Homework Equations The Attempt at a Solution I have already proved that the relation is reflexive and symmetric, but I'm unsure of my approach...

Homework Statement Let m and n be two integers. Prove that if m^2 + n^2 is divisible by 4, then both m and n are even numbers Homework Equations The Attempt at a Solution Proof by Contrapositive. Assume m, n are odd numbers, showing that m^2 + n^2 is not divisible by 4...