5883085
Description
Mind Map by Fazreel Yusman, updated more than 1 year ago
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Created by Fazreel Yusman
over 8 years ago
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How to
prove
conditional
statement?
- Direct Method
- if p then q
- outline
- example
- strategy.
- It’s the simplest way to prove
propositions that have the
form of conditional
statements.
- It’s the simplest way to prove
propositions that have the
form of conditional
statements.
- if p then q
- Indirect Method
- Contrapositive
- p -> q is logically equivalent to ~q -> ~p
- alternative to direct proof
- outline
- example
- strategy
- use when it’s too hard to prove using direct
method. (eg: p is more complicated than q)
- use when it’s too hard to prove using direct
method. (eg: p is more complicated than q)
- p -> q is logically equivalent to ~q -> ~p
- Contradiction
- prove it wrong
- outline
- example
- strategy
- use when both direct and
contrapositive method doesn’t work
- use when both direct and
contrapositive method doesn’t work
- prove it wrong
- Contrapositive
- Mathematical
Induction
- step
- prove it right
- inductive step
- inductive step
- prove it right
- outline
- example
- strategy
- : It’s used when we have a set
of statements and we need to
prove that they are all true. (eg:
S1, S2, S3, … Sn, …)
- : It’s used when we have a set
of statements and we need to
prove that they are all true. (eg:
S1, S2, S3, … Sn, …)
- step
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