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.

Answer:

2 รท 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.

Answer:

Given that all even numbers are in the two times table

2*x* must be an even number

(2*x*)^{2}

= 4*x*^{2}

= 2(2*x*^{2})

which must be in the two times table and is therefore even.

See also Geometric Proofs

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