inclusive disjunction

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If p and q are statements, then the statement ‘p or q’, denoted by pq, is the disjunction of p and q. For example, if p is ‘It is raining’ and q is ‘It is Monday’ then pq is ‘It is raining or it is Monday’. To be quite clear, notice that pq 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.

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