MAT 243 Online Written Homework Assignments for Week 3 (units 6-9) 1. Prove or disprove: = [1,3) (2,3] is the empty set. 2. Prove that if A and B are sets, . Your proof must be based on the exact definitions. 3. If : [ 2 , 2 ] [1,1]; () = cos(), find a. 1 ((0,1)) b. ( 1 ({1})). c. 1 ( ({ 2 })). d. Is it always true that if X is a subset of the domain of a function , then 1 (()) = ? You may treat common, precalculus-level knowledge of the cosine function, such as the graph of the function, as a given. You must explain your answers, but you do not need to prove them rigorously. 4. Prove that the function : (, 0] [1, ); () = 2 + 1 is bijective and find 1 . This means that you have to determine the domain and range of 1 as well as a formula for 1 (). 5. Prove that : ; () = 2 is not bijective. [ is the set of positive integers.] 6. Evaluate the sum and simplify as much as possible. Leave large exponential expressions of the form with a, b integers in that form in your final answer and do not evaluate them. 9000 =10 721 62+1 Show all your work. Do NOT give a calculator approximation or the exact integer answer as produced by a computer algebra system (though you may use such approaches to verify your answer.) 2017 R. Boerner ASU School of Mathematical and Statistical Sciences