# Mathematicalproving

### Description

Mind Map on Mathematical proving, created by Sharifah Huda on 06/07/2016.
Mind Map by Sharifah Huda, updated more than 1 year ago
 Created by Sharifah Huda almost 8 years ago
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## Resource summary

Mathematicalproving
1. Direct method
1. If p, then q ( p ---> q )
1. Outline
1. If r is a, then s is b
1. 1) suppose r is a
1. 2) then r = definition of a
1. 3) s = definition of a
1. 4) expand
1. 5) factorise
1. 6) relate s to definition of b
1. 7) therefore s is b
2. Example :-
1. Is m is an even integer, then 7m+4 is an even integer
1. 1) suppose m is an even integer
1. 2) then m = 2n
1. 3) 7m+4 = 7(2n)+4
1. 4) = 14n+4
1. 5) = 2(7n+2)
1. 6) = 2q, q=7n+2
1. 7) therefore 7m+4 is an even integer
3. Indirect method
1. Contrapositive
1. Not limited to conditional statement
1. conditional statement
1. example :
1. if [n^2]
2. outline :
1. proposition : p ---> q
1. assume p is true, q is false ( p ---> ~q )
1. then p --> q must be true
3. non conditional statement
1. proposition : p
1. assume ~ p is true
1. then p must be true
4. Mathematical induction

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