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.
answer ASAP
(I ) Given the following assumptions : P is True, Q is False, R...
answer ASAP
(I ) Given the following assumptions : P is True, Q is False, R
is True
Determine the final answer for the following propositions
1) P --> Q --> ~R
2) ( ~ P <---> ~ R ) V P
3) (P V Q V ) <---> R
(II) Given the following sets
A = { 1, 3, 5, 7, 9, 19, 29 }, B = { 1, 5, 3}, C = {7, 8, 14}, D
= {7,8,...
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...
In the following table task durations are given in weeks. Use
the three point to find:...
In the following table task durations are given in weeks. Use
the three point to find:
Activity
Predecessor
Optimistic
Normal
Pessimistic
A
None
2
4
6
B
None
3
5
9
C
A
4
5
7
D
A
4
6
10
E
B,C
4
5
7
F
D
3
4
8
G
E
3
5
8
Construct the (AON) Activity on Node network diagram
Find each activity’s ES, EF, LS and LS
Identify all paths. Which path is the critical...
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,...