Revision as of 16:06, 31 July 2020 by Mag1c (talk | contribs) (Statements: conditional inverse converse contrapositive)

Logic is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument.


A statement is either true or false, but it will never be both or neither. An example of statement can be "A duck is a bird." which is true. Another example is "A pencil does not exist" which is false.

===Conditional:=== If $P$ then $Q$.

===Inverse:=== If not $P$ then not $Q$.

===Converse:=== If $Q$ then $P$.

===Contrapositive:=== If not $Q$ then not $P$.

The conditional is equivalent to the contrapositive. The inverse is equivalent to the converse. When both the conditional and the converse are true at the same time, this is equivalent to an Iff statement.

Logical Notations

Main article: Logical notation

A Logical notation is a special syntax that is shorthand for logical statements.


The negation of $p$, denoted by $\neg p$, is the statement that is true when $p$ is false and is false when $p$ is true. This means simply "it is not the case that $p$."


The conjunction of two statements basically means "$p$ and $q$" and is denoted by $p \land q$.


The disjunction of two statements basically means "$p$ or $q$" and is denoted by $p \vee q$.


This operation is given by the statement "If $p$, then $q$". It is denoted by $p\implies q$. An example is "if $x+3=5$, then $x=2$.


The converse of the statement $p \implies q$ is $q \implies p$.


The contrapositive of the statement $p \implies q$ is $\neg q \implies \neg p$. These statements are logically equivalent.

Truth Tables

A truth table is the list of all possible values of a compound statement.


There are two types of quantifiers: A universal Quantifier: "for all" and an existential Quantifier: "there exists". A universal quantifier is denoted by $\forall$ and an existential quantifier is denoted by $\exists$.

See Also

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