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5846297
Mathematicalproving
Description
Mind Map on Mathematical proving, created by Sharifah Huda on 06/07/2016.
No tags specified
calculus
mathematics
fun
Mind Map by
Sharifah Huda
, updated more than 1 year ago
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Created by
Sharifah Huda
almost 8 years ago
24
0
0
Resource summary
Mathematicalproving
Direct method
If p, then q ( p ---> q )
Outline
If r is a, then s is b
1) suppose r is a
2) then r = definition of a
3) s = definition of a
4) expand
5) factorise
6) relate s to definition of b
7) therefore s is b
Example :-
Is m is an even integer, then 7m+4 is an even integer
1) suppose m is an even integer
2) then m = 2n
3) 7m+4 = 7(2n)+4
4) = 14n+4
5) = 2(7n+2)
6) = 2q, q=7n+2
7) therefore 7m+4 is an even integer
Indirect method
Contrapositive
Contradiction
Not limited to conditional statement
conditional statement
example :
if [n^2]
outline :
proposition : p ---> q
assume p is true, q is false ( p ---> ~q )
come across a contradiction
then p --> q must be true
non conditional statement
proposition : p
assume ~ p is true
come across a contradiction
then p must be true
Mathematical induction
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