Algebraic equivalence are rules applied in Maths to show that when two things are added or multiplied together, usually the relationship between even and odd numbers, a specific outcome is given.
The following rules apply for any even or odd numbers:
We prove all of these in a similar way.
To represent an even number, it is indicated as , where is any natural number. To represent an odd number, it is indicated as , where x is any natural number.
To prove , we take two even numbers, namely and , where and are natural numbers.
As we can factor a two out of the sum of and , it shows that it is also even and therefore it has been proven.
Key fact: proofs are not proofs if you try and use an example to prove a concept!