Mathematical logic and foundations Definition

Disjunction

Definition

Let $p$ and $q$ be propositions. The disjunction of $p$ and $q$ is the proposition $p \lor q$ , read " $p$ or $q$ ". The proposition $p \lor q$ is false when $p$ is false and $q$ is false. In all other cases, $p \lor q$ is true.

$p$	$q$	$p \lor q$
T	T	T
T	F	T
F	T	T
F	F	F

Remarks

This "or" is inclusive: $p \lor q$ is true when both $p$ and $q$ are true. The exclusive "or" is true when exactly one of $p$ and $q$ is true. The union of two sets uses disjunction: $x \in A \cup B$ means $x \in A \lor x \in B$ .

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Proposition concept
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Tag	`0H5GKDTB01`
URI	`m2://0H5GKDTB01`
Kind	definition
Writing	W1 stated
MSC	03B05
Defines	Disjunction
Uses	Proposition

Disjunction

Definition

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