Category:Implication
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This category contains results about Implication in the context of Propositional Logic.
Definitions specific to this category can be found in Definitions/Implication.
The conditional or implication is a binary connective:
- $p \implies q$
defined as:
- If $p$ is true, then $q$ is true.
This is known as a conditional statement.
A conditional statement is also known as a conditional proposition or just a conditional.
$p \implies q$ is voiced:
- if $p$ then $q$
or:
- $p$ implies $q$
Subcategories
This category has the following 43 subcategories, out of 43 total.
B
- Biconditional Elimination (9 P)
C
- Clavius's Law (10 P)
- Constructive Dilemma (6 P)
- Contradictory Antecedent (3 P)
- Contradictory Consequent (3 P)
D
- Destructive Dilemma (6 P)
E
- Examples of Formal Implication (empty)
F
- Factor Principles (23 P)
H
I
- Implication in terms of NAND (3 P)
L
- Law of Identity (14 P)
M
- Modus Ponendo Ponens (18 P)
P
- Peirce's Law (13 P)
- Praeclarum Theorema (6 P)
- Principle of Commutation (14 P)
- Principle of Composition (4 P)
- Principle of Dilemma (13 P)
- Proof by Cases (21 P)
- Proof by Contradiction (15 P)
R
- Rule of Exportation (12 P)
- Rule of Implication (9 P)
- Rule of Material Equivalence (7 P)
- Rule of Material Implication (16 P)
- Rule of Transposition (40 P)
S
T
- Tautological Antecedent (3 P)
- Tautological Consequent (3 P)
Pages in category "Implication"
The following 60 pages are in this category, out of 60 total.
C
- Clavius's Law
- Conditional and Converse are not Equivalent
- Conditional and Inverse are not Equivalent
- Conditional iff Biconditional of Antecedent with Conjunction
- Conditional iff Biconditional of Consequent with Disjunction
- Conditional is not Associative
- Conditional is not Commutative
- Conditional is not Right Self-Distributive
- Conditional/Semantics of Conditional/Examples
- Conjunction and Implication
- Conjunction Equivalent to Negation of Implication of Negative
- Conjunction with Negative Equivalent to Negation of Implication
- Constructive Dilemma
- Contradictory Antecedent
- Contradictory Consequent
- Converse of Conditional is Contrapositive of Inverse
- Converse of Conditional is Inverse of Contrapositive