CIS 1910 Lecture Notes - Lecture 3: Free Variables And Bound Variables, Universal Quantification

• School: University of Guelph
• Department: Computing and Information Science
• Course: CIS 1910
• Professor: Luiza Antonie

Document Summary

Quantifiers provide notation that allows to quantify (count) objects in the domain of the variable. If the domain is a finite set of elements a1, a2 ak then x p(x) p(a1) For the above proposition p(x) adding a universal quantifier in front of it implies that for all values of x in the domain, the proposition p(x) or (x+3=6) is true. Example: domain of x is all students in the course, predicate is p(x) completed homework x p(x) states that all students in the course completed the homework. Furthermore if jane, alex, bob are the only students in the class, the universally quantified propositions would read as jane completed the homework and alex completed the homework and. (backwards capital e) is the existential quantifier. Xp(x) means that there exists an x in the domain for which the predicate p holds true.