13387524
Description
Mind Map by Luke Byrne, updated more than 1 year ago
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Created by Luke Byrne
about 6 years ago
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Propositional Logic
- "A proposition is any declarative sentence which that is either true of false."
- CONNECTIVES
- ∧ - "and"
- T^T=T
- T^T=T
- ∨ - "or"
- inclusive or
- inclusive or
- ¬/~ - "not"
- → - "implies" (if/then)
- T->F=F
- T->F=F
- ↔ - iff (if and only if)
- TT/FF=T
- TT/FF=T
- Connective Priority in order below
- ∧ - "and"
- IMPORTANT TAUTOLOGIES
- De Morgan's Laws
- ¬ and ∨ can be used together to represent all connectives
- ¬ and ∨ can be used together to represent all connectives
- Sheffer's stroke ('|')
- P|Q (which stands for ”not both P and Q” or ”P nand Q”) can be used to represent all of ¬, ∧, ∨, →, ↔
since ¬P ↔ P|P and P ∨ Q ↔ (P|P) | (Q|Q).
- P|Q (which stands for ”not both P and Q” or ”P nand Q”) can be used to represent all of ¬, ∧, ∨, →, ↔
since ¬P ↔ P|P and P ∨ Q ↔ (P|P) | (Q|Q).
- Given P → Q...
- Converse
- Q → P
- Q → P
- Contrapositive
- ¬Q → ¬P
- ¬Q → ¬P
- Converse
- De Morgan's Laws
- Reductio ad absurdum
- √2 by contradiction
- √2 by contradiction
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