1. Consider the statement "If Ciscar eats Chinese food. then he drinks milk.\" a. Write the converse of the statement. in. Write the contrapositiue of the statement. c. Is it possible for the contrapositwe to be false? If it was, what would that tell you? d. Suppose the original statement is true, and that Ciscar drinks milk. Can you conclude anything [about his eating Chinese food}? Explain. e. Suppose the original statement is true. and that Ciscar does not drink milk. Can you conclude anything [about his eating Chinese food]? Explain. \f5. How many positive integers less than moo are multiples of 3, 5, or 7"? Explain your answer using the Principle of InclusionfExclusion. .1 Suppose you have 12 chips, each a different color. How many different stacks of 5 chips can you make? Explain your answer and why it is the same as using the formula for P(12, 5}. b. Using the scenario ofthe 12 chips again, what does 12! count? What does '3'! count? Explain. c. Explain why it makes sense to cliyicle12! by 1'! when computing P{12,5} {in terms of the chips}. d. Does your explanation work for numbers other than 12 and 5? Explain the formula Pm, k} = ("\"115 using the yariables n and k. 7. Use summation [Z] or product {H} notation to rewrite the following. a. 2+4++3+"'+2. b.1+5+g+13+'\"+425 l 1 l l C. 1+E++E+t\"+. d. 2*4' +++++ 271. E i%J(%}(i---i%- 8. Express 0454545 . . . as a fraction. 9. Use polynomial fitting to find the formula for the nth term of the sequence (admit. which starts, 3,?,14,24,. . . 10. Solve the recurrence relation a\" : an l + 2" with an : 5.