Connect chp 2
Let E be the set of students at your school majoring in engineering and let B be the set of students at your school majoring in business. Select all of the students from the list below who would be members of E ∪ B.
Dan, who is majoring in computer science and in business Scarlette, who is majoring in business Phoebe, who is majoring in both engineering and business Karson, who is majoring in engineering
Which of the following are true statements about the Cartesian product of {a, b} and {1, 2, 3}? (Select all that apply.)
The size of the Cartesian product is 6. (a, 3) is an element of the Cartesian product. (b, 1) is an element of the Cartesian product.
Which of the following are true statements about the Cartesian product of {a, b} and {1, 2, 3}? (Select all that apply.)
(b, 1) is an element of the Cartesian product. (a, 3) is an element of the Cartesian product. The size of the Cartesian product is 6.
Match the statement on the left with the task on the right needed to prove the statement.
A ⊆ B matches Choice Show that if x ∈ A, then x ∈ B. A ⊈ B matches Choice Find a single x ∈ A, such that x ∉ B. A = B matches Choice Show that A ⊆ B and B ⊆ A. A = ∅ matches Choice Show that A ⊆ ∅. A ≠ ∅ matches Choice Find a single x ∈ A.
Match the statement on the left with the task on the right needed to prove the statement.
A ⊆ B matches Choice Show that if x ∈ A, then x ∈ B. A ⊈ B matches Choice Find a single x ∈ A, such that x ∉ B. A = B matches Choice Show that A ⊆ B and B ⊆ A. A = ∅ matches Choice Show that A ⊆ ∅. A ≠ ∅ matches Choice Find a single x ∈ A.
Select all that are set identities.
A∩B�∩� = A� ∪ B� A ∪ U = U A∩(B∩C)�∩�∩� = (A∩B)∩C�∩�∩� A ∩ A = A A∪B�∪� = A� ∩ B� A ∩ ∅ = ∅ A∪(B∪C)�∪�∪� = (A∪B)∪C�∪�∪� A∩(B∪C)�∩�∪� = (A∩B)�∩� ∪ (A∩C)�∩� A ∪ ∅ = A A=A�=� A ∪ B = B ∪ A A∪(B∩C)�∪�∩� = (A∪B)�∪� ∩ (A∪C)�∪� A ∩ B = B ∩ A A ∪ A = A A ∩ A� = ∅ A∪(A∩B)=A�∪�∩�=� A∩(A∪B)=A�∩�∪�=� A ∪ A� = U
Which of the following are true statements? (Select all that apply.)
For every set S, S ⊆ S. For every set S, ∅ ⊆ S.
Which of the following are true statements? (Select all that apply.)
For every set S, ∅ ⊆ S. For every set S, S ⊆ S.
Match the symbol on the left with the set on the right.
Z matches Choice {..., -2, -1, 0, 1, 2,...} the set of integers Z+ matches Choice {1, 2, 3,... }, the set of positive integers Q matches Choice {p/q | p ∈ Z, q ∈ Z, and q ≠ 0}, the set of rational numbers Q+ matches Choice {p/q | p ∈ Z+, q ∈ Z+}, the set of positive rational numbers R matches Choice The set of real numbers R+ matches Choice The set of positive real numbers C matches Choice The set of complex numbers
Which of the following intervals contains both the integers -1 and 3? (Select all that apply.)
[-1, 5) [-1, 3] (-3, 3]
Which of the following are correct ways to describe the set of nonnegative integers less than or equal to 100 that are perfect cubes?
{ x | x is an integer, 0≤ x ≤ 100 and x is a perfect cube} { x | x = y3 where y is a nonnegative integer not exceeding 4} {0, 1, 8, 27, 64}
Match the sets on the left with a true statement about the Cartesian product of those sets on the right.
{1, 2} and {3, 4} matches Choice Its cardinality is 4. {1, 2, 3, 4} and {3, 4, 5, 6} matches Choice (4, 3) is a member. {4, 5, 6, 7} and {4, 5, 6, 7} matches Choice (5, 5) is a member. {a, e, i, o, u} and {b, g, t, d} matches Choice Its cardinality is 20. {1, 2, 3} and {1, 2, 4} matches Choice (2, 2) is a member.
Match the sets on the left with a true statement about the Cartesian product of those sets on the right.
{1, 2} and {3, 4} matches Choice Its cardinality is 4. {1, 2, 3, 4} and {3, 4, 5, 6} matches Choice (4, 3) is a member. {4, 5, 6, 7} and {4, 5, 6, 7} matches Choice (5, 5) is a member. {a, e, i, o, u} and {b, g, t, d} matches Choice Its cardinality is 20. {1, 2, 3} and {1, 2, 4} matches Choice (2, 2) is a member.
Rank the two sets by the size of their intersection, from smallest at the top to largest at the bottom.
{1,2,3,4,5},{6,7,8,9,10} {1,2,3,4,5},{5,6,7,8,9,10} {2,3,4,5,6},{5,6,7,8,9,10} {2,3,4,5,6},{2,3,4,5,6} {1,2,3,4,5,6,7,8},{3,4,5,6,7,8,9,10}
Match a set on the left with an alternate way of describing it on the right.
{2, 4, 6, 8, 10} matches Choice {x | x is a positive even integer not exceeding 10} {1, 2, 4, 8} matches Choice {x | x is a positive integer which is a power of 2, not exceeding 10} {2, 6, 10} matches Choice {x | x is a positive even integer not divisible by 4, and not exceeding 10} {0, 2, 4, 6, 8} matches Choice {x | x is a nonnegative even integer, less than 10}
Which of the following sets are finite? (Select all that apply.)
{Z} {Z, N, C, Q} ∅
Which of the following sets is the power set of {a, b, {c, d}}? (Select all that apply.)
{{a, b, {c, d}}, {a, b},{a, {c, d}},{b, {c, d}}, ∅, {a}, {b}, {{c, d}}} {∅, {a}, {b},{{c, d}}, {a, b}, {a, {c, d}}, {b, {c, d}},{a, b, {c, d}}}
Match the set on the left with its size on the right.
∅ 0 {∅,{∅}} matches Choice 2 {∅,∅} matches Choice 1 The set of letters in the English alphabet. matches Choice 26 {a, b, S}, where S is the set of letters in the English alphabet. matches Choice 3 Z matches Choice infinite
Match the set on the left with its size on the right.
∅ matches Choice 0 {∅,{∅}} matches Choice 2 {∅,∅} matches Choice 1 The set of letters in the English alphabet. matches Choice 26 {a, b, S}, where S is the set of letters in the English alphabet. matches Choice 3 Z matches Choice infinite
Which of the following are subsets of {∅, {∅}}? (Select all that apply.)
∅ {∅, {∅}} {∅} {{∅}}
