Definition
Disjunction
A disjunction is an “or” statement that is true when either part, or both parts, are true.
What it means
An “or” rule opens more than one way to qualify. One side can work, the other side can work, and usually both can work too.
Remember it
OR opens either door—and in mathematics both doors may be open.
Example
Consider “the number is less than 3 or even.” The number 1 makes the first part true, 8 makes the second part true, and 2 makes both parts true. All three satisfy the disjunction; 5 satisfies neither part.
Watch for
Everyday “either-or” sometimes means exactly one choice. Mathematical “or” normally includes the both-true case unless the problem excludes it.
Common mix-up
A conjunction uses “and” and requires every joined part to be true. A disjunction uses “or” and needs at least one true part.
Exact meaning
A disjunction joins two or more statements with logical “or.” In standard mathematical logic it is inclusive: the disjunction is true when at least one part is true, including when more than one part is true, unless “but not both” is stated.