MATH 290 Exam questions and answers with detailed accurate solutions available

What is a set? - ANSA collection of things. These things are called the elements of the set and they can be just about anything (pg. 3) Why are sets so important? - ANSBecause all of mathematics can be described with sets (pg. 3) What are elements? - ANSThe things that make up the set. They are separated by commas inside of braces (pg. 3) What is an infinite set? - ANSA set that has an infinite number of elements (pg. 3) What is a finite set? - ANSA set that has a finite number of elements (pg. 3) What makes two sets equal? Give an example - ANSIf they contain the exact same elements. {2,4,6,8} = {8,6,4,2}(pg. 3) How do we represent sets? - ANSUsually with uppercase letters e.g. A={1,3,5,7,9...} How do we symbolically say an element is part of a set? - ANSUsing the ∈ symbol. e.g. If S={a,b,c,d,e...} a∈S read "a is an element of S" or, "a is in S" or, "a in S." We could also say a,b,c∈S (pg. 3) Can only numbers be the elements of a set? - ANSNo, we can put letters, coordinates, sets, matrices and more inside of sets (see pg. 4) What is the cardinality of a set? - ANSIt's the number of unique elements a finite set has. AKA it's size. We symbolize cardinality with absolute value bars around the capital letter symbolizing the set (pg. 4) What is the empty set? - ANSIt's the set that has no elements. Symbolized by ∅. ∅={} (pg. 4) Is ∅={∅}? - ANSNo, think of it like boxes. An empty box is not the same thing as an box with an empty box inside of it. ∅ has a cardinality of zero while {∅} has a cardinality of one (pg. 4) What is set builder notation? - ANSIt's notation used to describe sets that are too big or complex to list between braces. X={expression: rule} where X is all the values of "expression" that are specified by "rule" e.g. E={2n : n∈Z} read, "E is the set of all things of form 2n, such that n is an element of the integers." (see pg. 5 example 1.1)