PropositionalFunction.md (972B)
1 # Propositional Function 2 3 U 1.4.1 4 5 **Definition:** A propositional function is a function that takes an arbitrary number of inputs and outputs a truth value. 6 7 An example of a propositional function is the function P(x) defined as 'x > 2'. This function could then be evaluated as follows: 8 9 1. P(1) | False 10 2. P(2) | False 11 3. P(3) | True 12 13 Once a propositional function is evaluated with some object(s) and no longer contains any variables, it is then said to be a proposition. 14 15 Given this, we know that the propositional function P(x,y) is still a propositional function when we specify P(1,y) because there is still a variable namely y. 16 17 An interesting thing about propositional functions with the universal quantifier is that if the universe (U) is empty, the proposition is true as there are no counterexamples. 18 19 ## Bound and Free 20 21 When we assign a variable of a propositional function it is said to be bound. Conversely, when a variable is not bound it is then free.