4. Let set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,...
4. Let set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20}
set A = numbers in U that divide into 12 with no remainder,
set B = numbers in U that divide into 16 with no remainder, and set
C = the numbers in U that divide into 20 with no remainder.
a. Made a Venn diagram showing the elements of the sets U, A,...
Given two sets A and B, the
intersection of these sets, denoted A ∩
B, is...
Given two sets A and B, the
intersection of these sets, denoted A ∩
B, is the set containing the elements that are in both
A and B. That is, A ∩ B =
{x : x ∈ A and x ∈
B}.
Two sets A and B are
disjoint if they have no elements in common. That
is, if A ∩ B = ∅.
Given two sets A and B, the union of
these sets, denoted A ∪ B,...
Let
U={1,2, 3, ...,3200}.
Let S be the subset of the numbers in U that are...
Let
U={1,2, 3, ...,3200}.
Let S be the subset of the numbers in U that are multiples of
4, and let T be the subset of U that are multiples of 9. Since
3200 divided by 4 equals it follows that
n(S)=n({4*1,4*2,...,4*800})=800
(a) Find n(T) using a method similar to the one that showed
that n(S)=800
(b) Find n(S∩T).
(c) Label the number of elements in each region of a two-loop
Venn diagram with the universe U and subsets S...
Problem 2.1 Which of the following are sets? Assume that a
proper universal set has been...
Problem 2.1 Which of the following are sets? Assume that a
proper universal set has been chosen and answer by listing the
names of the collections of objects that are sets. Warning: at
least one of these items has an answer that, while likely, is not
100% certain. (i) A = {2,3,5,7,11,13,19} (ii) B={A,E,I,O,U} (iii)
C={√x : x < 0} (iv) D = {1,2,A,5,B,Q,1,V} (v) E is the list of
first names of people in the 1972 phone book in...
Set Operations
In questions 7 and 8 Let A = {0, 2, 4, 6}, B =...
Set Operations
In questions 7 and 8 Let A = {0, 2, 4, 6}, B =
{0, 1, 2, 3}, and C = {4, 5, 6}. U = {x∈ℤ| 0≤x≤10}
7. Find (A ∪ B) – C’.
8. Find C ∩ (A’ ⊕ B’)
Venn Diagrams
Draw Venn diagrams for the following set operations. Show each
step and label the sets as well as what the diagram is showing Ex:
if the Venn diagram is showing C’, label the rectangle...
Let SS be the universal set, where:
S={1,2,3,...,28,29,30}S={1,2,3,...,28,29,30}
Let sets AA and BB be subsets of...
Let SS be the universal set, where:
S={1,2,3,...,28,29,30}S={1,2,3,...,28,29,30}
Let sets AA and BB be subsets of SS, where:
Set
A={1,8,13,14,16,17,20,25,27,28}A={1,8,13,14,16,17,20,25,27,28}
Set B={6,7,9,13,14,30}B={6,7,9,13,14,30}
Set
C={5,8,10,11,13,14,15,17,23,25,28}C={5,8,10,11,13,14,15,17,23,25,28}
Find the number of elements in the set (A∩B)(A∩B)
n(A∩B)n(A∩B) =
Find the number of elements in the set (B∩C)(B∩C)
n(B∩C)n(B∩C) =
Find the number of elements in the set (A∩C)(A∩C)
n(A∩C)n(A∩C) =
Using the following information to find the probability (p) of
a-e Universal set =
{1,2,3,4,5,6,7,8,9,12,13,14,16,20,22,44,48,50,52,56} Subset...
Using the following information to find the probability (p) of
a-e Universal set =
{1,2,3,4,5,6,7,8,9,12,13,14,16,20,22,44,48,50,52,56} Subset A =
{9,12,13,20,22,44,50,56} Subset H = {4,5,8,9,16,22,44,48,52} Subset
C = {1,4,20,22,44,48,52,56} Find: a.) P(AnH)UC' b.) P(HnC)' c.)
P(H)' d.) P[H\C]-P(H given C) e.) P[H\A]-P(H given A)
Let
U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
A = {5,...
Let
U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
A = {5, 7, 9, 11, 13},
B = {6, 8, 10, 12, 14},
and
C = {5, 6, 8, 9, 12, 13}.
List the elements of each set. (Enter your answers using roster
notation. Enter EMPTY or ∅ for the empty set.)
(a) Ac ∩ (B
∩ C c)
(b) (A ∪ Bc) ∪
(B ∩ C c)
(c) (A ∪
B)c ∩
C c