COMP 232 Lecture Notes - Lecture 3: Propositional Function, Asteroid Family

• School: Concordia University
• Department: Computer Sci.
• Course: COMP 232
• Professor: Gosta Grahne

Document Summary

The american city is polluted. are not propositions, since their truth values depend on the values of the variable involved. Nevertheless, we sometimes wish to make gen- eral statements: For this, we need to introduce new terminol- ogy. Consider the following statement involving an integer variable: x2 x + 2. The predicate x2 x+ 2 is a property of x. We denote x2 x + 2 by p(x). P is called a propositional function, its value depends on the value assigned to x. Assigning a speci c value to x in p(x) yields a proposition. P( 10) 100 10 + 2 true. Another way to make a proposition out of a propositional function is to use statements about how general the validity of a propositional func- tion is. The universe of discourse (uod) for p(x) speci es all possible values of x. P(x) is true for all values of x in the uod.