A mathematical argument is used to prove a statement is either true or false. There are two types of argument that you be asked to prove.
The easiest argument is to prove that a statement is false. Only one example needs to be provided to prove that the statement is false. Is the statement All prime numbers are odd numbers true or false? The number 2 is a prime number: therefore the statement is false.
The harder argument is to prove that a statement is always true. The argument moves through several steps - defining the assumptions, the construction of the argument, and the justification for the statement being true.
Prove that the statement Dividing any number by another number will result in a smaller number is false.
Any similar example would do.
2 ÷ 0.5 = 4
4 is larger than 2 so the statement is false
Prove that squaring an even number will always result in an even number.
Given that all even numbers are in the two times table
2x must be an even number
which must be in the two times table and is therefore even.
See also Geometric Proofs