Mathematicalproving

Description

Mind Map on Mathematical proving, created by Sharifah Huda on 06/07/2016.
Sharifah Huda
Mind Map by Sharifah Huda, updated more than 1 year ago
Sharifah Huda
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. Contradiction
              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. come across a contradiction
                            1. then p --> q must be true
                    3. non conditional statement
                      1. proposition : p
                        1. assume ~ p is true
                          1. come across a contradiction
                            1. then p must be true
                    4. Mathematical induction
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