1. Suppose Z={a,{a},{a,b}}. a. What is the cardinality of Z ? b. What is the power set of Z ? c. Indicate clearly which of the following statements are true. i. {a,b}Z ii. aZ iii {a}Z iv. {a}Z v. bZ vi. {a,b}Z 2. Define the following sets: A={milk,coffee}B={bacon,ham}C={eggs,pancakes} List the elements of ABC. Note that elements of a cross product are ordered tuples. 3. Define the following sets: A={1,2,3}B={1,2} Recall that elements of the cross product of two sets are ordered pairs. a. Give one element of AB that is not in BA, or explain why no such element exists. b. Give one element of BA that are not in AB, or explain why no such element exists. c. How many elements are there in AB ? d. How many elements are there in BA ? e. Explain why AA is or is not a subset of AB. 4. Give two positive integers m and n such that 11m+n=11m+11n or explain why no such integers exist. 5. Evaluate the following: a. m=050m b. k=01003+5k c. Does j=01003j=j=11003i? Justify your answer. 6. Give the next five terms (s2,s3,s4,s5,s6) of the following sequences. You can assume that the sequences start with an index of 1 . i. An arithmetic sequence in which s1=1 and the common difference is 3 . ii. A geometric sequence in which s1=7 and the common ratio is 5 . 7. Suppose S={1} and T={a,b}, and recall that a function from a set S to a set T can be specified as a subset of the cross product ST. a. Specify as a subset of the cross product ST an onto function from S to T, or explain why no such function exists. b. Specify as a subset of the cross product ST a one-to-one function from S to T, or explain why no such function exists