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
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Implication can refer to:

• Logic:
• Logical implication as regarded in mathematical logic.
• Material conditional as regarded in philosophical logic.

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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
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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
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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.
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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.
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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
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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.
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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 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
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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.
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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.
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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
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material nonimplication is the negation of implication. p⊅q

Definition

Truth table

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"

Properties

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In logic, converse nonimplication is a logical connective which is the negation of the converse of implication.

Definition

p⊄q which is the same as ~(p ← q)

Truth table

The truth table of p ⊄ q.
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