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.