homework 3 - 3.1/1-5, 10, 22, 23, 37, 41, 50 1. Let S =...

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3.1/ 1-5, 10, 22, 23, 37, 41, 50 1. Let S = {2, 5, 17, 27}. Which of the following are true? a. 5 œ S b. 2 +5 œ S c. {} œ S d. S œ S Note that 2 + 5 = 7, which is not in S . There are no sets that are elements of S , so {} and S can't be in S 2. Let B = { x | x œ and -1 < x < 2}. Which of the following are true? a. 0 œ B b. -1 œ B c. -0.84 œ B d. 2 œ B Note that -1 is not less than -1, and that 2 is not in 3. How many different sets are described in the following? What are they? {2, 3, 4} set A { } set B { x | x is the first letter of cat, bat or apple} set C { x | x is the first letter of cat, bat and apple} set B { x | x œ N and 2 <= x <= 4} set D {2, a , 3, b , 4, c } set E {a, b, e} set F {3, 4, 2} set D Note that since no letter can be the first letter of cat, bat and apple, that set is empty. 4. Describe each of the following sets by listing its elements: a. { x | x œ and x 2 < 25} {0, 1, 2, 3, 4} b. { x | x œ and x is even and 2 < x < 11} {4, 6, 8, 10} c. { x | x is one of the first three presidents of the United States} {Washington, Adams, Jefferson} d. { x | x œ and x 2 = -1} e. { x | x is one of the New England states} {Maine, Vermont, New Hampshire, Massachusetts, Rhode Island, Connecticut} f. { x | x œ and | x | < 4} {-3, -2, -1, 0, 1, 2, 3} 5. Describe each of the following sets by listing its elements: a. { x | x œ and x 2 – 5 x + 6 = 0} {2, 3} b. { x | x œ and x 2 = 7} {} c. { x | x œ and x 2 - 2 x - 8 = 0} {4} (note that -2 is not in ) 10. Let A = { x | x œ and 1 < x < 50}, B = { x | x œ and 1 < x < 50}, C = { x | x œ and |x | ¥ 25} Which of the following statements are true? a. A Œ B b. 17 œ A c. A Œ C 5 is in A , but not in C d. -40 œ C e. 3 œ B f. {0, 1, 2} Œ A 0 is not in A g. {} œ B I don't see any empty sets listed as an element of B , do you? h.{ x | x œ Z and x 2 ¥ 625} Œ C 22. Find P (S) for S = {1, 2, 3, 4}. How many elements do you expect to have? We would expect 2 4 subsets. They are: {}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, . .. , {1, 2, 3, 4}. 23. Find P (S) for S = { f }. P ({ f }) = {{}, { f }}
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37. Let A = { p, q, r, s }, B = { r, t, v } and C = { p, s, t, u } be subsets of S = { p, q, r, s, t, u, v, w }. Find a. B C { t } b. A » C { p, q, r, s, t, u } c. C ' { q, r, v, w } d. A B C {} e. B – C { r, v } f. ( A » B )' { u, w } g. A µ B {( p,r ), ( p,t ), ( p,v ), ( q,r ), ( q,t ), ( q,v ), ( r,r ), ( r,t ), ( r,v ), ( s,r ), ( s,t ), ( s,v )} h. ( A » B ) C ' { q, r, v } 41. Let A = { x | x is a word that appears before dog in an English Dictionary} B = { x | x is a word that appears after canary in an English Dictionary} C = { x | x is a word of more than four letters} Which of the following are true statements? a.
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homework 3 - 3.1/1-5, 10, 22, 23, 37, 41, 50 1. Let S =...

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