TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false. Tell whether the statement is true or false. 2) {2, 9, 13} = {0, 2, 9, 13} 3) {x | x is a counting number greater than 38} = {38, 39, 40, ...} MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find n(A) for the set. 4) A = {0, 2, 4, 6, 8} A) n(A) = 2 5) A = {x∣x ∈ N and 14 ≤ x ≤ 22} A) 36 B) 7 C) 37 D) 9 B) n(A) = 8 C) n(A) = 4 D) n(A) = 5 5) 4) 2) 3)

Determine whether the sets are equal, equivalent, both, or neither. 6) {L, M, N, O} and {l, m, n, o} A) Neither B) Equivalent C) Both D) Equal 7) C) Equal D) Neither 6)

7) {first, second, third} and {1, 2, 3} A) Both B) Equivalent

TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false. Let A = {1, 3, 5, 7} B = {5, 6, 7, 8} C = {5, 8} D = {2, 5, 8} U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the statement is true or false. 8) {0} ⊆ U 9) { } ⊂ C 8) 9)

1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. If the statement is true for all sets A and B, answer ʺtrue.ʺ If it is not true for all sets A and B, answer ʺfalse.ʺ Assume that A ≠ ∅, U ≠ ∅, and A ⊂ U. 10) B ⊆ B A) True 11) ∅ ⊄ ∅ A) True Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 12) (A ∩ B)ʹ A) {t, v, x} C) {s, u, w} Construct a Venn diagram illustrating the following sets. 13) U = {a, b, c, d, e, f, g, h, i,j , k, l, m, n, o, p} A = {a, e, i, o} B = {b, c, d, f, g, h, j, k, l, m} C = {a, b, c, d, e, f, g} 13) B) {q, s, t, u, v, w, x, y} D) {r, t, u, v, w, x, z} 12) B) False B) False 11) 10)

A)

B)

2

C)

D)

Use the Venn diagram shown to list the set in roster form.

14) A ∩ C A) {11, 13} C) {2, 3, 4, 6, 8, 9, 10, 11, 12, 13} Solve the problem. 15) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans, and 17 like both red and green jelly beans. How many of the students surveyed like no green jelly beans? A) 17 B) 30 C) 21 D) 38 B) {4, 11, 12} D) {11}

14)

15)

Show that the set is infinite by placing it in a one -to-one correspondence with a proper subset of itself. Be sure to show the pairing of the general terms in the sets. 16) {3, 10, 17, 24, ...} A) { 3, 10, 17, 24, ..., 7n + 4, ...} ↓ ↓ ↓ ↓ ↓ { 10, 17, 24, 31, ..., 7n + 3, ...} C) { 3, 10, 17, 24, ..., 7n - 4, ...} ↓ ↓ ↓ ↓ ↓ { 10, 17, 24, 31, ..., 7n + 2, ...} B) { 3, 10, 17, 24, ..., 7n - 4, ...} ↓ ↓ ↓ ↓ ↓ { 10, 17, 24, 31, ..., 7n + 3, ...} D) { 3, 10, 17, 24, ..., 7n - 10, ...} ↓ ↓ ↓ ↓ ↓ { 10, 17, 24, 31, ..., 7n - 3, ...} 16)

3

Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets. 17) {3, 7, 11, 15, ...} A) { 1, 2, 3, 4, ..., n, ...} ↓ ↓ ↓ ↓ ↓ { 3, 7, 11, 15, ..., 4n + 1, ...} C) { 1, 2, 3, 4, ..., n, ...} ↓ ↓ ↓ ↓ ↓ { 3, 7, 11, 15, ..., 4n - 1, ...} Construct a truth table for the statement. 18) (t ∧ p) ∨ (~t ∧ ~p) A) t T F p F T (t ∧ p) ∨ (~t ∧ ~p) F F B) t T T F F D) t T T F F p T F T F p T F T F (t ∧ p) ∨ (~t ∧ ~p) F F T T (t ∧ p) ∨ (~t ∧ ~p) T...