Question

Explain the inter definability of truth functions

Answer 1

a truth function[1] is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values. The typical example is in propositional logic, wherein a compound statement is constructed by one or two statements connected by a logical connective; if the truth value of the compound statement is determined by the truth value(s) of the constituent statement(s), the compound statement is called a truth function, and the logical connective is said to be truth functional.[2]

Classical propositional logic is a truth-functional propositional logic,[3] in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function.[4] On the contrary, modal logic is non-truth-functional.