Generated From Textbook

Question 1

What is the union of sets A and B if A = {1,4,9} and B = {1,3,6,10}?

Answer 1

AUB = {1, 3, 4, 6, 9, 10}

Union of two sets combines all unique elements from both sets.

Question 2

What is the intersection of sets A and B if A = {1,4,9} and B = {1,3,6,10}?

Answer 2

AnB = {1}

Intersection of two sets includes only the elements common to both sets.

Question 3

What is the difference A B if A = {1,4,9} and B = {1,3,6,10}?

Answer 3

A \ B = {4, 9}

The difference A \ B consists of elements in A that are not in B.

Question 4

What is the difference B A if A = {1,4,9} and B = {1,3,6,10}?

Answer 4

B \ A = {3, 6, 10}

The difference B \ A consists of elements in B that are not in A.

Question 5

If C = (B ∩ C) ∪ (C ∩ A), what is this expression referring to?

Answer 5

C = (B ∩ C) ∪ (C ∩ A)

This expression combines the intersections of sets B and C, and C and A.

Question 6

Find the least element of the set {n ∈ N : n² - 3 > 2}.

Answer 6

Least element = 3

Solve the inequality n² - 3 > 2 to find n.

Question 7

Find the least element of the set {n ∈ N : n² - 5 ∈ N}.

Answer 7

Least element = 3

n must be such that n² - 5 is a non-negative integer.

Question 8

Find the least element of the set {n² + 1 : n ∈ N}.

Answer 8

Least element = 2

The smallest value occurs at n = 1.

Question 9

What is the cardinality of the set A = {4, 5, 6, …, 37}?

Answer 9

|A| = 34

Count the integers from 4 to 37 inclusive.

Question 10

What is the cardinality of the set A = {x ∈ Z : -2 < x < 100}?

Answer 10

|A| = 101

Count integers from -1 to 99 inclusive.

Question 11

What is the cardinality of the intersection AnB if A = {x ∈ N : x ≤ 20} and B = {x ∈ N : x is prime}?

Answer 11

|AnB| = 8

Count the prime numbers less than or equal to 20.

Question 12

Find a set of largest possible size that is a subset of both {1, 2, 3, 4, 5} and {2, 4, 6, 8, 10}.

Answer 12

Largest subset = {2, 4}

The intersection of both sets.

Question 13

Find a set of smallest possible size that has both {1, 2, 3, 4, 5} and {2, 4, 6, 8, 10} as subsets.

Answer 13

Smallest subset = {1, 2, 3, 4, 5, 6, 8, 10}

This set must include all elements from both sets.

Question 14

What is the largest possible cardinality of set C if A = {n ∈ N : 20 < n < 50} and B = {n ∈ N : 10 < n ≤ 30}?

Answer 14

Largest cardinality of C = 10

C must be a subset of both A and B.

Question 15

How many sets C have the property that C ⊆ A and B ⊆ C if A = {1, 2, 3, 4, 5} and B = {2, 3, 4}?

Answer 15

Number of sets C = 8

C must include all elements of B and can include any combination of remaining elements from A.

Question 16

Find AnB if A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}.

Answer 16

AnB = {3, 4, 5}

Intersection includes elements common to both sets.

Question 17

Find AUB if A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}.

Answer 17

AUB = {1, 2, 3, 4, 5, 6, 7}

The union includes all unique elements from both sets.

Question 18

Find A B if A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}.

Answer 18

A \ B = {1, 2}

The difference includes elements in A that are not in B.

Question 19

Find An (B ∪ C) where A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, and C = {2, 3, 5}.

Answer 19

An (B ∪ C) = {2, 3, 4, 5}

Intersection of A with the union of sets B and C.

Question 20

Find AnB if A = {x ∈ N : 4 < x < 12} and B = {x ∈ N : x is even}.

Answer 20

AnB = {6, 8, 10}

Elements of A that are also even.

Question 21

Find A B if A = {x ∈ N : 4 < x < 12} and B = {x ∈ N : x is even}.

Answer 21

A \ B = {5, 7, 9, 11}

Elements in A that are not even.

Question 22

Find AnB if A = {x ∈ N : 3 < x ≤ 13} and B = {x ∈ N : x is even}.

Answer 22

AnB = {4, 6, 8, 10, 12}

Elements of A that are also even.

Question 23

Find AUB if A = {x ∈ N : 3 < x ≤ 13} and B = {x ∈ N : x is even}.

Answer 23

AUB = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

The union combines all unique elements from both sets.

Question 24

Find B ∩ C if B = {x ∈ N : x is even} and C = {x ∈ N : x is odd}.

Answer 24

B ∩ C = {}

There are no common elements between even and odd numbers.

Question 25

Find B ∪ C if B = {x ∈ N : x is even} and C = {x ∈ N : x is odd}.

Answer 25

B ∪ C = {x ∈ N} ## Footnote The union includes all natural numbers.

Question 26

Provide an example of sets A and B such that AnB = {3, 5}.

Answer 26

Example: A = {3, 5, 7}, B = {5, 3, 8} ## Footnote Both sets must include 3 and 5, and can include other elements.