Compound statements

Many statements we meet are not simple, single ideas but are built by joining two or more smaller statements together with connecting words such as "and" and "or". Such a statement is called a compound statement.

Definition. A compound statement is one that is made up of two or more statements, each of which — on its own — is called a component statement of the compound one.

For example, p: "There is something wrong with the bulb or with the wiring" is built from two component statements joined by "or":

• q: There is something wrong with the bulb.
• r: There is something wrong with the wiring.

Similarly, p: "7 is an odd number" and q: "7 is a prime number" can be joined with "and" to give the compound statement r: "7 is both odd and a prime number." …