ECE103 Midterm: Sets and Quantifiers

• School: University of Waterloo
• Department: Electrical and Computer Engineering
• Course: ECE103
• Professor: Martin Pei

Document Summary

A collection of objects, which are the elements of the set. We write a a to denote that a is an element of a. For a set a, the number of elements of a is denoted. |a| and is called either the cardinality or size of a. A = |{1, 2, 3}|, size = 3. Given two sets a and b, if every element of a is also an element of b, then a is a subset of b denoted by a b. A b is equivalent to x (x a x b) Given two sets a and b, there are several other sets that can be obtained from them. Union a b, which is x a b if and only if x a. Intersection a b, which is x a b if and only if x a and x b. Cartesian product a b, which consists of all the ordered pairs (a, b), with a a and b b.