#5-14, #25-29Sorry for all the questions I just hate spending 3 dollars per question. Thank you for all the help.
Problem Set 2.4 Level 1 24. a. If A represents the letters in the English alphabet, what 1. IN YOUR OWN WORDS Why do you think the fundamental is the cardinality of A? counting principle is so "fundamental"? b. If B represents the number of U.S. states, what is the cardinality of B? 2. IN YOUR OWN WORDS Describe your preconceived c. What the cardinality of the set containing the sets A notions about "infinity." Next, describe your understanding and B? of "infinity" in light of the material in this section. 25. If A = { letters of the alphabet } and B = {U.S. states], what is 3. IN YOUR OWN WORDS What is the Cartesian product of two sets? A X B ? 4. IN YOUR OWN WORDS What does the cardinality of the 26. If A = {letters of the alphabet ), what is |A X A |? Cartesian product have to do with the fundamental counting 27. If C = (500, 501, 502, . . ., 599 ] and D = (U.S. state capitals ], principle? what is | C X D|? Find the Cartesian product of the sets given in Problems 5-10. 28. If M = { distinct letters in the word mathematics } and N = { distinct letters in the word nevertheless ), what is 5. A = {c, d, f } and B = {w, x]; find A X B. MX N ? 1234561 8 6. A = (c, d, f ] and B = (w, x]; find B X A. 29. Show that there is more than one one-to-one correspondence 7. F = {1, 2, 3, 4, 5} and C = (a, b, c}; between the sets {m, a, t} and { 1, 2, 3 }. find F X C. 30. Show that the following sets have the same cardinality, by 8. F = {1, 2, 3, 4, 5} and C = (a, b, c}; placing the elements into a one-to-one correspondence. find C X F. (1, 2, 3, 4, . .., 999, 1000} 9. X = {x|x E N, x is between 1 and 5 } and (7964, 7965, 7966, 7967, . .., 8962, 8963} V = {vlv is a vowel}; find X X V. 31. Show that the following sets do not have the same cardinality. 10. X = {x/x E N, x is between 1 and 5 ] and (1, 2, 3, 4, ..., 586, 587} V = {vlv is a vowel }; find V X X. (550, 551, 552, 553, . .., 902, 903 } 32. Do the following sets have the same cardinality? Give the cardinality of each set in Problems 11-20. (48, 49, 50, . . ., 783, 784} 11. {48, 49, . .., 189, 190] 12. { 16, 20, 24, . . ., 400, 404} (485, 487, 489, . .., 2053, 2055] 13. {-42, -41, . . ., 41, 42) 14. {-998, -997, . . ., 85, 86} 33. Classify the following sets as finite or infinite. 15. {100, 200, 300, . .. } 16. (2, 3. 4. 3,..} a. The set of stars in the Milky Way 17. T X W where T = {1, 2, . .., 19, 20 }, W = (a, b, . . ., v, w} 18. S X V where S = {U.S. states }, V = (a, b, c} 19. {x x is an odd integer} 20. {yly is an even integer} Level 2 21. a. What is the cardinality of the empty set? b. Write the question and answer in part a using mathematical Caltech/JPL/NASA notation. 22. a. What is the cardinality of the set containing the empty set? Milky Way Galaxy b. Write the question and answer in part a using mathematical b. The set of counting numbers greater than two million notation. 23. a. What is the cardinality of a set containing the number 0? 34. Classify the following sets as finite or infinite. b. Write the question and answer in part a using mathematical a. The set of people who are living or who have ever lived b. The set of grains of sand on all the beaches on Earth notation
