## Quick Reference

If *p* and *q* are statements, then the statement ‘*p* or *q*’, denoted by *p* ∨ *q*, is the disjunction of *p* and *q*. For example, if *p* is ‘It is raining’ and *q* is ‘It is Monday’ then *p* ∨ *q* is ‘It is raining or it is Monday’. To be quite clear, notice that *p* ∨ *q* means ‘*p* or *q* or both’: the disjunction of *p* and *q* is true when at least one of the statements *p* and *q* is true. The truth table is therefore as follows:

This is sometimes explicitly known as ‘inclusive disjunction’ to distinguish it from exclusive disjunction which requires exactly one of *p*, *q* to be true.

See also exclusive disjunction.

*Subjects:*
Mathematics.