5846297
Beschreibung
Mindmap von Sharifah Huda, aktualisiert more than 1 year ago
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Erstellt von Sharifah Huda
vor mehr als 8 Jahre
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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
- 7) therefore s is b
- 6) relate s to definition of b
- 5) factorise
- 4) expand
- 3) s = definition of a
- 2) then r = definition of a
- 1) suppose r is a
- If r is a, then 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
- 7) therefore 7m+4 is an
even integer
- 6) = 2q, q=7n+2
- 5) = 2(7n+2)
- 4) = 14n+4
- 3) 7m+4 = 7(2n)+4
- 2) then m = 2n
- 1) suppose m is an even integer
- Is m is an even integer, then 7m+4 is
an even integer
- If p, then q (
p ---> q )
- Indirect
method
- Contrapositive
- Contradiction
- Not limited to
conditional statement
- conditional statement
- example :
- if [n^2]
- 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
- then p --> q must be
true
- come across a
contradiction
- assume p is true, q is
false ( p ---> ~q )
- proposition : p ---> q
- example :
- non conditional statement
- proposition : p
- assume ~ p is true
- come across a contradiction
- then p must be true
- then p must be true
- come across a contradiction
- assume ~ p is true
- proposition : p
- Not limited to
conditional statement
- Mathematical
induction
- Contrapositive
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