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 mainproduct.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 it has 23= 8 subsets.h. subsets: {1,4,5} {1,4} {1,5} {4,5} {1} {4} {5} { }i. {1,4,5} is not a proper subset because it is equal to the set C.j. Is {4, 1, 5}  C? Yes, because it is equal to C.Is {4, 1, 5}  C? No, because it is not a proper subset of C (proper subset means inside but not equal to C)4. (A  B)  C is not equivalent to A  (B  C):(A  B) is regions I, II, III, IV, V, VI (B  C) is regions V, VIC is regions IV, V, VI, VII C is regions IV, V, VI, VII So they intersect at regions IV, V So the union is in regions IV, V, VI, VII.The resulting final regions are not the same.5. A'  C is not equivalent to (B  C)'  A:A' is regions III, VI, VII, VIII (B  C) is regions II, III, IV, V, VI, VIIC is regions IV, V, VI, VII (B  C)' is regions I, VIII So they intersect at regions VI, VII A is regions I, II, IV, VSo the intersection is in regions I.The resulting final regions are not the