For problems 1 through 11, use the following sets. The set U is the universal set. 0- -32, - 8, -2, - 3, 1, 4, 16, 64) N-1,2,4,8) U= {-32,-8,-2, .. 1, 2, 100-, 8. 1004. 10003, 64) S-2245, 1000,, B16) 1. Write set B in roster notation. 2. Write set O in set-builder notation 3. Write the number of subsets of N in binary 4. Write the number of proper subsets of U in hexidecimal. 5. Convert each element of S to base-ten (decimal) 6. How many two-way intersections of the sets B. O. N u. and S exist? (e.g. Nno, ons, etc) 7. If -47

Question

I only need the explanation of number 9. I am not sure how to do it. Thanks

For problems 1 through 11, use the following sets. The set U is the universal set.
0- -32, - 8, -2, - 3, 1, 4, 16, 64)
N-1,2,4,8)
U= {-32,-8,-2, .. 1, 2, 100-, 8. 1004. 10003, 64)
S-2245, 1000,, B16)
1. Write set B in roster notation.
2. Write set O in set-builder notation
3. Write the number of subsets of N in binary
4. Write the number of proper subsets of U in hexidecimal.
5. Convert each element of S to base-ten (decimal)
6. How many two-way intersections of the sets B. O. N u. and S exist? (e.g. Nno, ons, etc)
7. If -47<x 71 and xE Z, What is p(r E O)?
8. Consider the following four relations, f, g, h, and j. For each, draw an arrow diagram. Then tell
whether it is a function or not. If not, why not? If it is, tell whether it is one-to-one, onto, and/or a
bijection. Are any of these functions equal? Recall that Z3 [0,1,2)
j : N → 73 , J(y) = (y2-2y+1)mod3
9. Determine whether each of the following 5 statements is True or False
(BNN = φ) V (-32ES)
(27ES) A (SE2)
(0 2)
(BEB) V -(Bcu)

Image Transcription

For problems 1 through 11, use the following sets. The set U is the universal set. 0- -32, - 8, -2, - 3, 1, 4, 16, 64) N-1,2,4,8) U= {-32,-8,-2, .. 1, 2, 100-, 8. 1004. 10003, 64) S-2245, 1000,, B16) 1. Write set B in roster notation. 2. Write set O in set-builder notation 3. Write the number of subsets of N in binary 4. Write the number of proper subsets of U in hexidecimal. 5. Convert each element of S to base-ten (decimal) 6. How many two-way intersections of the sets B. O. N u. and S exist? (e.g. Nno, ons, etc) 7. If -47<x 71 and xE Z, What is p(r E O)? 8. Consider the following four relations, f, g, h, and j. For each, draw an arrow diagram. Then tell whether it is a function or not. If not, why not? If it is, tell whether it is one-to-one, onto, and/or a bijection. Are any of these functions equal? Recall that Z3 [0,1,2) j : N → 73 , J(y) = (y2-2y+1)mod3 9. Determine whether each of the following 5 statements is True or False (BNN = φ) V (-32ES) (27ES) A (SE2) (0 2) (BEB) V -(Bcu)

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