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 =...
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...
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...
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
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
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}
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...