1. |
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Two sets in which the same elements are listed in different orders are the same. |
2. |
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The same element can never appear twice in a set. |
3. |
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The empty set is a subset of itself. |
4. |
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If two sets are not equal, then one is a subset of the other. |
5. |
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If (A B) = A, then (A B) = B. |
6. |
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If (A B) = (A B), then A = B. |
7. |
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(A B)' = (A' B'). |
8. |
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The number of possible outcomes when five coins are tossed, and the list of heads and tails is noted, is 10. |
9. |
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The number of possible outcomes when three dice are thrown, and the list of numbers is noted, is 216. |
10. |
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There are 5! possible lists of five different names. |
11. |
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There are 5! possible sets of five different names. |
12. |
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There are more sets of 5 chosen from 7 than there are sets of 2 chosen from 7. |
13. |
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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. |
14. |
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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. |
15. |
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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." |
16. |
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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." |
17. |
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In a hand of poker, a pair of 10's is more likely to come up than a full house. |
18. |
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The number of lists of r objects chosen from n is always divisible by r!. |
19. |
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The number of sets of r objects chosen from n is always divisible by r!. |
20. |
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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). |