The following strings are propositional formulas under the signature:
(i)both 0-place connectives are formulas
(ii)for any binary connective ⨀, if f and g are formulas then (f⊙g) is a formula.
A propositional formula is a particular kind of syntactic formula that is well-formed and has a truth value in propositional logic. A propositional formula yields a distinct truth value when all of the variables' values are known. A propositional formula may alternatively be referred to as a phrase, a propositional expression, or a sentential formula.
Simple statements like "five is greater than three" or propositional variables like p and q are combined to build a propositional formula using connectives or logical operators like NOT, AND, OR, or IMPLIES.
The term "proposition" is frequently used in mathematics to refer to a propositional formula, but in reality, a propositional formula is a formal expression that signifies a proposition.
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