2.3 Practice

Question 1

Given U = natural numbers from 1 to 10 inclusive; A = {1, 2, 3, 8}; B = {1, 3, 6, 7, 8}; C = { }
Find A ∩ B

Answer 1

A ∩ B = {1, 3, 8}

Question 2

Given U = natural numbers from 1 to 10 inclusive; A = {1, 2, 3, 8}; B = {1, 3, 6, 7, 8}; C = { }
Find A∩C

Answer 2

A∩C = { }

Question 3

Given U = natural numbers from 1 to 10 inclusive; A = {1, 2, 3, 8}; B = {1, 3, 6, 7, 8}; C = { }
Find A’∩B

Answer 3

A’∩B = {6, 7}

Question 4

Given U = natural numbers from 1 to 10 inclusive; A = {1, 2, 3, 8}; B = {1, 3, 6, 7, 8}; C = { }
Find (A∩B)’

Answer 4

(A∩B)’ = {2, 4, 5, 6, 7, 9, 10}

Question 5

Given A∪B = {1, 2, 3}
Find n(A∪B)

Answer 5

n(A∪B) = 3 (cardinal numbers in set)

Question 6

Given the sets: 𝑈 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔}; 𝐴 = {𝑎, 𝑏, 𝑒, 𝑔}; 𝐵 = {𝑎, 𝑐, 𝑑, 𝑒}; 𝐶 = {𝑏, 𝑒, 𝑓}
Find (𝐴 ∪ 𝐵) ∩ (𝐴 ∪ 𝐶)

Answer 6

(𝐴 ∪ 𝐵) ∩ (𝐴 ∪ 𝐶) = {a, b, e, g}

Question 7

Given the sets: 𝑈 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔}; 𝐴 = {𝑎, 𝑏, 𝑒, 𝑔}; 𝐵 = {𝑎, 𝑐, 𝑑, 𝑒}; 𝐶 = {𝑏, 𝑒, 𝑓}
Find (𝐴 ∪ 𝐵) ∩ 𝐶’

Answer 7

(𝐴 ∪ 𝐵) ∩ 𝐶’ = {a, c, d, g}

Question 8

Given A = {a, b, c} B = {a, d, e, f}
Find n(𝐴 ∪ 𝐵)

Answer 8

6

Question 9

Use the general addition rule. The results of a survey of customers at a McDonald’s restaurant showed that 28 purchased either a hamburger or french fries, 20 purchased french fries, and 17 purchased both a hamburger and french fries. How many customers purchased only a hamburger?

Answer 9

H = hamburger
F = french fries
n(H∪F) = n(H) + n(F) - H∩F
28 = n(H) + 20 - 17
n(H)= 25

Question 10

Given sets 𝑈 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔, ℎ, 𝑖,𝑗, 𝑘}, 𝐴 = {𝑏, 𝑑, 𝑒, 𝑓, 𝑔, ℎ}, 𝐵 = {𝑎, 𝑏, 𝑑, ℎ, 𝑖}, and 𝐶 = {𝑏, 𝑒, 𝑔}
Determine 𝐴 − 𝐶 and 𝐴’ − 𝐵.

Answer 10

A - C = {d, f, h}
A’ - B = {c, j, k}

Question 11

Given A = {orange, banana, apple} and B = {1, 2},
determine the following: 𝐴 × 𝐵
and 𝐵 × 𝐴

Answer 11

A × B = {(orange, 1), (orange, 2), (banana, 1), (banana, 2), (apple, 1), (apple, 2)}
B × A = {(1, orange), (1, banana), (1, apple), (2, orange), (2, banana), (2, apple)}