Name:______________________ KO 4/02Math 136 Test 365 pointsPlease answer on separate paper.1. Let U = The set of all kids in the first grade at Weston ElementaryA = all kids in the first grade reading group at Weston Elementary= {Sam, Marya, Edith, Janet, Leo, Marybeth, Miguel, Lika}B = The set of all kids in the first grade reading group at Weston Elementarywhose names begin with MC= The set of all kids in the first grade math groupa. Is B  A? Explain why or why not.b. Do you think it is always true that C  A? Sometimes true? Never true? Draw Venn diagrams and use words to explain.c. Use words to describe (AC)’d. How many subsets does set B have? Show how you know, using the correct formula.e. List all the subsets of Bf. Which of the above subsets is not a proper subset?2. In a survey of 230 zoos across the United States, it was found that50 kept their animals in cages85 kept their animals in natural habitats72 kept some animals in a petting zoo20 had petting zoos and kept their animals in cages25 kept their animals in a combination of cages and natural habitats5 had petting zoos and natural habitats2 used all three types of living arrangementsa. Sketch a Venn diagram to describe the situation. Fill in all appropriate numbers.b. A company is planning a wildlife park that only houses animals in their natural habitats (not in cages or petting zoos) How many zoos in this survey use that kind of arrangement?c. How many zoos did not use any of the above types of living arrangement?3. Use the numbered regions to show whether (AB) is equivalent to (C'B). Show your work by listing the numbered regions for each part of the problem.U A B I II III IVV VI VII C VIII4. Given the following statement: “It is not the case that I saw a flying saucer or that I should not watch theTV show ‘X-Files’ all the time.”a. Translate the statement into symbols. Clearly list what each symbol stands for.b. Use DeMorgan’s law to rewrite the symbols.c. Write your new statement in words. Does it mean the same thing as the original statement? Explain.5. Write a truth table for the following: ~ (p  q)  ~q6. a. Translate each of these arguments into symbols:i. If I don’t wake up early, I don’t get to work on time. I didn’t wake up early Therefore, I didn’t get to work on time.ii. If I don’t wake up early, I don’t get to work on time. I got to work on time Therefore, I woke up early.b. Are either (or both) of these arguments valid? Explain why or why not, based on the law of detachment or using the contrapositive.c. Write a truth table for one of the arguments. Based on the truth table, is the argument valid? (Does this change your answer for part b?)KO 02/04Math 136 Sets Test ReviewAnswers at end.1. In a survey of 200 shoppers at Supreme Supermarket, it was found that50 liked the French Roast Coffee85 liked the Cinnamon Blend Coffee70 liked Turkish Delight Coffee20 liked the French and the Cinnamon Blend Coffees35 liked the Cinnamon and the Turkish Coffees25 liked the Turkish and the French Coffees5 liked all three types of coffee.a. Sketch a Venn diagram to describe the situation. Fill in all appropriate numbers.b. A company wants to market a new coffee blend. To help them out, how many people in the survey liked only the Cinnamon Blend and not the others?c. How many did not like any of the coffees?d. If C is the set of people who liked Cinnamon Blend and T is the set who liked Turkish Delight, describe C  T ’ using words (use the description of the set and whichever words are appropriate: therefore, or, then, not, etc.)e. Use symbols and the letters for the appropriate sets to describe all coffee drinkers who like Turkish Delight or French Coffee but not Cinnamon Blend.2. In a survey of 50 farms in the Midwest, it was found that30 used chemical pesticides34 were large farms17 produced milk as a main product20 were large farms that used chemical pesticides15 were large farms that produced milk as their main product.5 used chemical pesticides and produced milk as their main product.3 were large farms, used chemical pesticides, and produced milk as a main product.a. Sketch a Venn diagram to describe the situation. Fill in all appropriate numbers.b. Organic farms do not use chemical pesticides. How many farms in the survey fit that description?c. An environmental group wants to encourage farmers to stop using bovine growth formula to increase milk production. They decide to send information packets out to all the small farms that produce milk as a main product, because they believe small farms may be easier to convince at first. How many information packets do they need?3. Let U = The set of all integers from 1 to 10, inclusiveA = The set of all even integers in UB = The set of all odd integers in UC = {1, 4, 5}a. Is C  A? Explain why or why not.b. Find A  B.c. Find A  C'd. Find A  B.e. Find A  C'f. Find (A  C)' Caution: not the same as previous problem.g. How many subsets does set C have? Show how you know without writing all the subsets down.h. Write all the subsets of C.i. Which of the subsets you listed is not a proper subset? Explain.j. Is {4, 1, 5}  C? Is {4, 1, 5}  C? Explain.4. Find whether (A  B)  C is equivalent to A  (B  C), using the numbered regions:UA BI II III IV V VI VIIIVIICShow all your work.5. Find whether A'  C is equivalent to (B  C)'  A, using the numbered regions:UA BI II III IV V VI VIIIVIICShow all your work.Answers1a. b. 35U c. 200-(all numbers)=70F C d. People who like cinn. blend and do not like10 15 35 Turkish Delight.e. (T  F)  C ’ 20 5 30 7015T2a. b. 2 + 12 + 6 = 20U c. small farms = not largeC L There are only 2 that are not large and produce8 17 2 milk. 2 3 12 60M3. a. No, all the elements of C are not in A. C overlaps with A, but it is not a subset (a subset must be entirely inside)b. A={2, 4, 6, 8, 10}, B ={1, 3, 5, 7, 9}, so A  B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (all the elements that are in A or B)c. A={2, 4, 6, 8, 10} C'={2, 3, 6, 7, 8, 9, 10}, so A  C' ={2, 3, 4, 6, 7, 8, 9, 10} d. A  B = { } (the empty set, since A and B not not have any elements in common.e. A  C' = {2, 6, 8, 10}f. A  C = {4} (where A overlaps with C) so (A  C)' = {1, 2, 3, 5, 6, 7, 8, 9, 10} (all but 4)g. C has 3 elements, so …