Let A, B, and C be sets in a universal set U. We are given n(U)...
Let A, B, and C be sets in a universal set U. We are given n(U)
= 63, n(A) = 33, n(B) = 34, n(C) = 28, n(A ∩ B) = 15, n(A ∩ C) =
17, n(B ∩ C) = 14, n(A ∩ B ∩ CC) = 9. Find the following
values.
(a) n(AC ∩ B ∩ C)
(b) n(A ∩ BC ∩ CC)
If U={−2,−1,3,4,5,7.5,8,8.3,9,12,15,16}, A={−1,4,7.5,9,12,15},
and B={−2,−1,4,7.5,8,9,16}. Find AC∪BC using De Morgan's law and a
Venn diagram.
If U={−2,−1,3,4,5,7.5,8,8.3,9,12,15,16}, A={−1,4,7.5,9,12,15},
and B={−2,−1,4,7.5,8,9,16}. Find AC∪BC using De Morgan's law and a
Venn diagram.
1. From experience, the manager of OSU Book Mart
knows that 40% of the people who are...
1. From experience, the manager of OSU Book Mart
knows that 40% of the people who are browsing in the store will
make a purchase.
(a) What is the probability that, among ten people who are
browsing in the store, exactly 3 will make a purchase.
(b) Explain why this is a binomial experiment.
2.
Given the Venn diagram , find the following and type
your answers into the box provided. Clearly mark each answer.
(a) n(A∪Bc)n(A∪Bc)
(b) n[A∩(B∪C)c]n[A∩(B∪C)c]
(c) n(Ac)n(Ac)
(d) n[(A∪B∪C)c]n[(A∪B∪C)c]
(e) n(Ac∪Bc∪Cc)n(Ac∪Bc∪Cc)
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...
(a) Suppose A, B and D are sets with the following
properties:
A ∩ B =...
(a) Suppose A, B and D are sets with the following
properties:
A ∩ B = A, B ∩ D =
D , ( Ac ∪
Dc)c = ∅
Draw a venn diagram for these sets and hence
shade the region
( Ac \ Bc) ∩ Dc
(b) Given that P(A U B) = k, P( A ) = 0.4, P( B ) =
0.2, determine the value of k if
(i) A and B are
independent....
(a) Suppose A, B and D are sets with the following
properties:
A ∩ B =...
(a) Suppose A, B and D are sets with the following
properties:
A ∩ B = A, B ∩ D =
D , ( Ac ∪
Dc)c = ∅
Draw a venn diagram for these sets and hence
shade the region
( Ac \ Bc) ∩ Dc
(b) Given that P(A U B) = k, P( A ) = 0.4, P( B ) =
0.2, determine the value of k if
(i) A and B are
independent....
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,...
1) Draw a Venn Diagram to show and list the set: If A = {1, 5,...
1) Draw a Venn Diagram to show and list the set: If A = {1, 5,
7, 6}, B = {2, 3, 6, Bob} and C = {Mary, 7, 6, 3}, then what is
(B∪A)∩C?
2) What is B x A where A = {headache, stress} and B = {homework,
test}.
3) A local cafe is offering free samples for thirteen different
coffee flavors. After sampling, the customer must rank the flavors
in order of preference. What are the chances...