Please help me and explain these problems to me. Thank you very much! I'm going to study that for exam.

Section 2.1: Use set builder notation to give a description of each of these sets: (0,3, 6, 9, 12) b) {-3, -2, -1, 0, 1, 2, 3) c) m, n, o, p) 2. Section 2.1: What is the cardinality of each of these sets? a) 0 b) (0) c) to, 10)) d) to, to), to, to))) 3. Section 2.2: Prove that if A and B are sets, than AUA(AnB) A. 4. Section 2.2: Draw a Venn diagram for the symmetric difference of the sets A and B 5. Section 2.3: Consider these functions from the set of students in a discrete mathematics class. Under what is the function one-to-one if it assigns to a student his or her a) mobile phone number b) student identification number. c) final grade in the class. d) home town. 6. Section 2.3: Show that if x is a real number, then Ixl lxl ifx is not an integer and Ixel 0 ifx is an integer 7. Section 2.4: What is the term asof the sequence (an) if an equals a) 2n-1? b) 7? c) 1 (-1)n? d) -(-20n? 8. Section 2.4: An employee joined a company in 2009 with a starting salary of $50,000. Every year this employee receives a raise of S1000 plus 5% of the salary of the previous year. a) Set up a recurrence relation for the salary of this employee n years after 2009. b) What will the salary of this employee be in 2017? c) Find an explicit formula for the salary of this employee n years after 2009. 9. Section 2.5: Determine whether each of these sets is finite, countably infinite, or uncountable. For any that are countably infinite, give a one-to-one correspondence between the that set and the set of positive integers. a) the integers greater than 10 b) the odd negative integers c) the integers with absolute value less than 1,000,000 10. Section 2.6: Show that matrix addition is commutative; that is, show that ifA and B are both m x n matrices, than A+B B+A. 11. Section 2.6: Let A be a zero-one matrix. Show that AVA A and AAA