True/False Quiz for Chapter 5

Sets and Counting

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1. Two sets in which the same elements are listed in different orders are the same. True False

2. The same element can appear twice in a set. True False

3. The empty set is not a subset of itself. True False

4. If two sets are not equal, then one is a subset of the other. True False

5. If (A B) = A, then (A B) = B. True False

6. If (A B) = (A B), then A = B. True False

7. (A B)' = (A' B'). True False

8. The number of possible outcomes when five coins are tossed, and the list of heads and tails is noted, is 10. True False

9. The number of possible outcomes when three dice are thrown, and the list of numbers is noted, is 216. True False

10. There are 5! possible lists of five different names. True False

11. There are 5! possible sets of five different names. True False

12. There are more sets of 5 chosen from 7 than there are sets of 2 chosen from 7. True False

13. The following counting procedure is valid in forming a three-letter sequence using the letters a, a, b. Step 1: Choose the first letter. Step 2: Choose the second letter. Step 3: Choose the third letter. True False

14. The following counting procedure is valid in forming a three-letter sequence using the letters a, a, b. Step 1: Place the first a. Step 2: Place the second a. Step 3: Place the b. True False

15. There are 10 people whose names begin with "A" and 12 people whose names begin with "O." Thus there are a total of 120 people whose names begin either with "A" or "O." True False

16. There are 10 people whose names begin with "A" and 12 people whose names begin with "O." Thus there are a total of 22 people whose names begin either with "A" or "O." True False

17. In a hand of poker, a pair of 10's is more likely to come up than a full house. True False

18. The number of lists of r objects chosen from n is always divisible by r!. True False

19. The number of sets of r objects chosen from n is always divisible by r!. True False

20. In a group of 339 people, at least two of them have the same first-name and last-name initials, possibly switched (as in Constance Smith and Selwyn Crown). True False