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Proof Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Mathematical proof
A logical argument that demonstrates a mathematical statement is always true.
Counterexample
An example that disproves a mathematical statement by showing it is not always true.
Even number
A number that can be expressed as 2n, where n is an integer.
Odd number
A number that can be expressed as 2n + 1, where n is an integer.
Prove a number is divisible by 3
Show that the number can be written as 3n, where n is an integer.
Prove a number is a multiple of 4
Show that the number can be written as 4n, where n is an integer.
Sum of two even numbers
The sum of two even numbers is always even because (2n) + (2m) = 2(n + m).
Sum of two odd numbers
The sum of two odd numbers is always even because (2n + 1) + (2m + 1) = 2(n + m + 1).
Sum of an even and an odd number
The sum of an even and an odd number is always odd because (2n) + (2m + 1) = 2(n + m) + 1.
Disproving a statement
To disprove a statement, provide a counterexample that shows the statement is not always true.
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