ITM 107 Lecture Notes - Lecture 1: Venn Diagram, Visu, Idempotence

• School: Ryerson University
• Department: Information Technology Management
• Course: ITM 107
• Professor: debashishroy

Document Summary

De nition: two sets are equal if they contain the same elements. I. e. , sets a and b are equal if. Recall: sets are unordered and we do not distinguish between repeated elements. {1, 1, 1} = {1}, and {a, b, c} = {b, a, c}. De nition: a set a is a subset of set b, denoted. A b, if every element x of a is also an element of b. That is, a b if x(x a x b). Notation: if set a is not a subset of b, we write a 6 b. De nition: if a b and a 6= b, we say that a is a proper subset of b. Note: one way of proving that a = b is by proving that a b and b a. De nition: the set that contains no elements is the empty set, and is denoted by or less commonly, {}. Theorem: prove that for every set s, s.