Propositional function
A propositional function in logic, is a sentence expressed in a way that would assume the value of true or false, except that within the sentence is a variable (x) that is not defined or specified, which leaves the statement undetermined. Of course, the sentence can consist of several such variables (e.g. n variables, in which case the function takes n arguments). As a mathematical function, A(x) or A(x1, x2, · · ·, xn), the propositional function is abstracted from predicates or propositional forms. As an example, let's imagine the predicate, "x is hot". The substitution of any entity for x will produce a specific proposition that can be described as either true or false, even though "x is hot" on its own has no value as either a true or false statement. However, when you assign x a value, such as lava, the function then has the value true; while if you assign x a value like ice, the function then has the value false.