obsidian/🛡️ Debate/📚 Coaching/📖 Coursework/Propositional Logic Intro.md

Operators & Symbols

Symbol	Operation	Example	Description
→	Implies	P→Q	A proposition that is only false if either Q is false or both P and Q are false.
↔	Biconditional	P↔Q	A proposition that denotes logic equivalence, and is true when both predicates are either true or false.
¬	Negation	¬P	A proposition that is true if and only if P is false.
∧	Conjunction	P∧Q	A proposition that is true if and only if both P and Q are true.
∨	Disjunction	P∨Q	A proposition that is false if and only if both P and Q are false.
⊻	Exclusive Or	P⊻Q	A proposition that is true if and only if either only P or only Q are true.
∀	Universal Quantifier	∀x(Px)	A proposition that states that for all x, P is true.
∃	Existential Quantifier	∃x(Px)	A proposition that states that there is at least one X, such that P(x) is true.
∴	Therefore	∴Q	The conclusion of a syllogism
:=	Definition	P:=grass is green	A general symbol used for defining propositions.
()	Parentheses	(P∧Q)	A means of grouping propositions together.

Logical Necessity

Tautology

P	True
T	T
F	T

Logical Impossibility

Contradiction

P	¬P	P∧¬P
T	F	F
F	T	F

Logical Possibility

Implication (P→Q)

P	Q	P→Q
T	T	T
T	F	F
F	T	T
F	F	T

Biconditional (P↔Q)

P	Q	P↔Q
T	T	T
T	F	F
F	T	F
F	F	T

Conjunction (P∧Q)

P	Q	P∧Q
T	T	T
T	F	F
F	T	F
F	F	F

Disjunction (P∨Q)

P	Q	P∨Q
T	T	T
T	F	T
F	T	T
F	F	F

Exclusive Disjunction (P⊻Q)

P	Q	P⊻Q
T	T	F
T	F	T
F	T	T
F	F	F

Esoteric Logical Possibility

Not And (P⊼Q)

P	Q	P⊼Q
T	T	F
T	F	T
F	T	T
F	F	T

Not Or (P⊽Q)

P	Q	P→Q
T	T	F
T	F	F
F	T	F
F	F	T

Material Nonimplication (P↛Q)

P	Q	P→Q
T	T	F
T	F	T
F	T	F
F	F	F

Converse Nonimplication (P↚Q)

P	Q	P→Q
T	T	F
T	F	F
F	T	T
F	F	F

Hashtags

#coursework #logic_course #propositional_logic