even numbers | MathCelebrity Forum

even numbers

1. If a is an even integer and b is an odd integer then prove a − b is an odd integer

If a is an even integer and b is an odd integer then prove a − b is an odd integer Let a be our even integer Let b be our odd integer We can express a = 2x (Standard form for even numbers) for some integer x We can express b = 2y + 1 (Standard form for odd numbers) for some integer y a - b =...
2. Prove there is no integer that is both even and odd

Let us take an integer x which is both even and odd. As an even integer, we write x in the form 2m for some integer m As an odd integer, we write x in the form 2n + 1 for some integer n Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1...
3. Prove the sum of two odd numbers is even

Take two arbitrary integers, x and y We can express the odd integer x as 2a + 1 for some integer a We can express the odd integer y as 2b + 1 for some integer b x + y = 2a + 1 + 2b + 1 x + y = 2a + 2b + 2 Factor out a 2: x + y = 2(a + b + 1) Since 2 times any integer even or odd is always...
4. n^2+n = odd

n^2+n = odd Factor n^2+n: n(n + 1) We have one of two scenarios: If n is odd, then n + 1 is even. The product of an odd and even number is an even number If n is even, then n + 1 is odd. The product of an even and odd number is an even number
5. n^2-n = even

n^2-n = even Factor n^2-n: n(n - 1) We have one of two scenarios: If n is odd, then n - 1 is even. The product of an odd and even number is an even number If n is even, then n - 1 is odd. The product of an even and odd number is an even number
6. Set of 2 digit even numbers less than 40

Set of 2 digit even numbers less than 40 Knowns and givens: 2 digit numbers start at 10 Less than 40 means we do not include 40 Even numbers are divisible by 2 {10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}
7. Set C is the set of two-digit even numbers less than 56 that are divisible by 5

Two digit Numbers less than 56: {10, 11, 12, ..., 55} Two Digit Even Numbers of that Set: {10, 12, 14, ..., 54} Two Digit Even numbers Divisible by 5 C = {10, 20, 30, 40, 50} Note: Even means you can divide it by 2 with no remainder. Divisible by 5 means the number ends in 5 or 0. Since it is...