Compound statement is a #202204281244 that consists of at least one primitive logical operator#. It expresses the relationship between different statements or the statement itself. For example: “is not \(p\)”, “\(p\) and \(q\)”, “\(p\) or \(q\) or both” and “\(p\) or \(q\) but not both”.
To express “is not \(p\)”, we could denote it mathematically as \(\sim p\) or \(\neg p\). This is called negation where we negate the statement itself. The truth value of a negation is the opposite truth value of the statement that it negated.
“\(p\) and \(q\)” can be expressed in terms of mathematic as \(p \land q\). The conjunction is true, if and only if both statements are true.
There are two kinds of or, an inclusive one and another exclusive, both are disjunction. The statement “\(p\) or \(q\) or both” uses inclusive or, where either \(p\), \(q\) or both are true, then the statement is true. It is denoted \(p \lor q\). “\(p\) or \(q\) but not both” uses in a more restrictive or where having both is not desirable. This could be express by only using \(\sim\), \(\land\) and \(\lor\): \((p \lor q) \land \sim (p \land q)\). It can shorten as \(p \oplus q\) to represent an exclusive or.
Their relationship could be expressed in 202205061151#.
There are more of it: