# Converse implication

Converse implication is the converse of implication. It takes the following forms:
• p⊂q
• p←q

## Definition

### Truth table

The truth table of p⊂q

p q ?
TTT
TFT
FTF
FFT

### Venn diagram

The Venn Diagram of "If B then A"

## Properties

truth-preserving: The interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true' as a result of converse implication.

## Natural language

### Rhetorical

"Not q without p."

## Computer Science

Conversion is a concept in traditional logic referring to a "type of immediate inference in which from a given proposition another proposition is inferred which has as its subject the predicate of the original proposition and as its predicate the subject of the original proposition
Implication can refer to:
• Logic:
• Logical implication as regarded in mathematical logic.
• Material conditional as regarded in philosophical logic.

A truth table is a mathematical table used in logic — specifically in connection with Boolean algebra, boolean functions, and propositional calculus — to compute the functional values of logical expressions on each of their functional arguments, that is, on each
Venn diagrams are illustrations used in the branch of mathematics known as set theory. They show all of the possible mathematical or logical relationships between sets (groups of things).
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The material conditional, also known as the material implication or truth functional conditional, expresses a property of certain conditionals in logic. In propositional logic, it expresses a binary truth function ⊃ from truth-values to truth-values.
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In propositional logic, a tautology (from the Greek word ταυτολογία) is a sentence that is true in every valuation (also called interpretation) of its propositional variables, independent of the truth values assigned to these
In logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical inversions of each other.

In logic and mathematics, negation or not is an operation on logical values, for example, the logical value of a proposition, that sends true to false and false to true.
In logic and/or mathematics, logical conjunction or and is a two-place logical operation that results in a value of true if both of its operands are true, otherwise a value of false!

## Definition

Logical conjunction
or, also known as logical disjunction or inclusive disjunction is a logical operator that results in true whenever one or more of its operands are true. In grammar, or is a coordinating conjunction.
The material conditional, also known as the material implication or truth functional conditional, expresses a property of certain conditionals in logic. In propositional logic, it expresses a binary truth function ⊃ from truth-values to truth-values.
In logic and mathematics, logical biconditional (sometimes also known as the material biconditional) is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and
exclusive disjunction, also called exclusive or, (symbolized XOR or EOR), is a type of logical disjunction on two operands that results in a value of "true" if and only if exactly one of the operands has a value of "true.
logical nor or joint denial is a boolean logic operator which produces a result that is the inverse of logical or. That is, (not or), p NOR q is only true when both p and q are false.
The Sheffer stroke, written "|" or "↑", in the subject matter of boolean functions, propositional calculus, sentential calculus, or zeroth order logic denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary
material nonimplication is the negation of implication. p⊅q

## Definition

p q ?
T T F
T F T
F T F
F F F

### Venn diagram

The Venn Diagram of "It's not the case that A implies B"