Page 24 - DMTH403_ABSTRACT_ALGEBRA

Unit 1: Generating Sets

Self Assessment Notes

1. Let A = {2, {4, 5}, 4}. Which statement is correct?
(a) 5 is an element of A.

(b) {5} is an element of A.
(c) {4, 5} is an element of A.
(d) {5} is a subset of A.

2. Which of these sets is finite?
(a) {x | x is even}
(b) {x | x < 5}
(c) {1, 2, 3,...}
(d) {1, 2, 3,...,999, 1000}

3. Which of these sets is not a null set?
(a) A = {x | 6x = 24 and 3x = 1}
(b) B = {x | x + 10 = 10}

(c) C = {x | x is a man older than 200 years}
(d) D = {x | x < x}
4. Let D E. Suppose a D and b E. Which of the following statements must be true?
(a) c  D
(b) b  D

(c) a  E
(d) a  D
5. Let A = {x | x is even}, B = {1, 2, 3... 99, 100}, C = {3, 5, 7, 9}, D = {101, 102} and E = {101, 103,
105}. Which of these sets can equal S if S A and S and B are disjoint?
(a) A (b) B (c) C
(d) D (e) E

6. Which statement best describes the Venn diagram below?
(a) A = B
(b) A and B are not comparable
(c) A  B
(d) A  B

7. Which set S does the power set 2 = {, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?
S
(a) {{1},{2},{3}}
(b) {1, 2, 3}
(c) {{1, 2}, {2, 3}, {1, 3}}

(d) {{1, 2, 3}}

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