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...
Definition 1. The symmetric difference of two sets A and B is
the set A△B defined...
Definition 1. The symmetric difference of two sets A and B is
the set A△B defined by A△B = (A \ B) ∪ (B \ A).
(a) Draw the Venn diagram for the symmetric difference.
(b) Prove that A△B = (A ∪ B) \ (A ∩ B).
(c) Prove A△A = ∅, A△∅ = A.
(d) Prove that for sets A, B, we have A△B = A \ B if and only if B
⊆ 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,...
(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....
(10) Consider the following property: For all sets A, B and C,
(A-B)∩(A-C)=A-(B∪C)
a. Construct a...
(10) Consider the following property: For all sets A, B and C,
(A-B)∩(A-C)=A-(B∪C)
a. Construct a proof of this property using set definitions.
b. Prove this property using a set-membership table, clearly
stating how the table proves the property.
c. Illustrate this property using Venn diagrams, clearly stating
how the diagram proves the property. You must use a separate Venn
diagram for the set on the left hand side of the equal sign, and
for the set on the right...
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,...
The next set of questions use the following example:
A network consists of the activities in...
The next set of questions use the following example:
A network consists of the activities in the following list.
Times are given in weeks.
CAN ONLY BE ONE OF THE OPTIONS it's not 5 I tried that.
Activity
Preceding
Time
A
--
8
B
--
3
C
A
7
D
A,B
3
E
C
4
F
D
6
Draw the network diagram.
Calculate the ES, EF, LS, LF, and Slack for each activity.
Find the total project completion time.
What...