#$&*
course Mth 151
02/06/11 - 15:01
'access: 01-77-150'name: Adrianne Hansome
'title: Chapter 2.3 QA
003. Intersection, Union, Complement, de Morgans Laws
*********************************************
Question: `q001. Note that there are 5 questions in this assignment.
Again we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair
and bright eyes. Let A stand for the collection of people who have dark hair and B for the collection who have bright eyes. The
Intersection of these two collections is denoted A ^ B, and stands for the collection of all people who have both dark hair and bright
eyes. The Union of these two collections is denoted A U B, and stands for the collection of all people who have at least one of these
characteristics. In terms of the diagram you made for the preceding problem, describe the collection A ^ B and the collection A U B.
Give the number of people in each of these collections (these numbers are designated by the notation n ( A ^ B) and n(A U B) ). Refer
to the diagrams you have made.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
(A^B) contains 8 elements. All elements have both dark hair and bright eyes.
(AUB) = Total # of people in room-35 minus (A^B)- 8 or 27 people
confidence rating #$&*: Very confident
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q002. Continuing the preceding example, we let A' stand for the people who are not in the collection A, and we let B' stand
for the people who are not in the collection B. What are the characteristics of the people in A', and what characterizes people in B' ?
What are n(A ') and n(B '), the numbers of people in A' and B' ?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
A' is the collection of people who have bright eyes. These are the 7 people in B + A^B or 15 people
B' is the collection of people who have dark hair . These are the 12 people in A + A^B or 20 people
confidence rating #$&*: Fairly Confident. Not sure when to leave items in the intersection out of calculation.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q003. ( A U B ) ' stands for the everyone outside A U B, and ( A ^ B ) ' stands for everyone outside A ^ B. What
characterizes the people in each of these collections, and how many people are there in each?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION: AUB' is everyone who has neither dark hair nor bright eyes or 8 people
A^B' is everyone who has neither characteristic and everyone who has 1 of the characteristics or 27 people
confidence rating #$&*: Fairly Confident.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q004. How many people are in A ' U B ', and how could those people be characterized? Answer the same for A ' ^ B '.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
A'UB' = 8 people. They are the people outside A and outsidegoe
A'^B'= 27 people. They are the parts of A and B that is not AUB and A' and B'
confidence rating #$&*: Not really confident on this one
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q005. Succinctly describe the relationships between ( A U B ) ', A ' U B ', (A ^ B) ' and A ' ^ B '.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
(AUB)' = A'^B'. This is the collection outside of (AUB)
(A^B)' = A'UB'. This is the collection outside of (A^B)
confidence rating #$&*: Very confident
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course Mth 151
02/06/11 - 15:01
'access: 01-77-150'name: Adrianne Hansome
'title: Chapter 2.3 QA
003. Intersection, Union, Complement, de Morgans Laws
*********************************************
Question: `q001. Note that there are 5 questions in this assignment.
Again we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair
and bright eyes. Let A stand for the collection of people who have dark hair and B for the collection who have bright eyes. The
Intersection of these two collections is denoted A ^ B, and stands for the collection of all people who have both dark hair and bright
eyes. The Union of these two collections is denoted A U B, and stands for the collection of all people who have at least one of these
characteristics. In terms of the diagram you made for the preceding problem, describe the collection A ^ B and the collection A U B.
Give the number of people in each of these collections (these numbers are designated by the notation n ( A ^ B) and n(A U B) ). Refer
to the diagrams you have made.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
(A^B) contains 8 elements. All elements have both dark hair and bright eyes.
(AUB) = Total # of people in room-35 minus (A^B)- 8 or 27 people
confidence rating #$&*: Very confident
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q002. Continuing the preceding example, we let A' stand for the people who are not in the collection A, and we let B' stand
for the people who are not in the collection B. What are the characteristics of the people in A', and what characterizes people in B' ?
What are n(A ') and n(B '), the numbers of people in A' and B' ?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
A' is the collection of people who have bright eyes. These are the 7 people in B + A^B or 15 people
B' is the collection of people who have dark hair . These are the 12 people in A + A^B or 20 people
confidence rating #$&*: Fairly Confident. Not sure when to leave items in the intersection out of calculation.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q003. ( A U B ) ' stands for the everyone outside A U B, and ( A ^ B ) ' stands for everyone outside A ^ B. What
characterizes the people in each of these collections, and how many people are there in each?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION: AUB' is everyone who has neither dark hair nor bright eyes or 8 people
A^B' is everyone who has neither characteristic and everyone who has 1 of the characteristics or 27 people
confidence rating #$&*: Fairly Confident.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q004. How many people are in A ' U B ', and how could those people be characterized? Answer the same for A ' ^ B '.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
A'UB' = 8 people. They are the people outside A and outsidegoe
A'^B'= 27 people. They are the parts of A and B that is not AUB and A' and B'
confidence rating #$&*: Not really confident on this one
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q005. Succinctly describe the relationships between ( A U B ) ', A ' U B ', (A ^ B) ' and A ' ^ B '.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
(AUB)' = A'^B'. This is the collection outside of (AUB)
(A^B)' = A'UB'. This is the collection outside of (A^B)
confidence rating #$&*: Very confident
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!
#$&*
course Mth 151
02/06/11 - 15:01
'access: 01-77-150'name: Adrianne Hansome
'title: Chapter 2.3 QA
003. Intersection, Union, Complement, de Morgans Laws
*********************************************
Question: `q001. Note that there are 5 questions in this assignment.
Again we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair
and bright eyes. Let A stand for the collection of people who have dark hair and B for the collection who have bright eyes. The
Intersection of these two collections is denoted A ^ B, and stands for the collection of all people who have both dark hair and bright
eyes. The Union of these two collections is denoted A U B, and stands for the collection of all people who have at least one of these
characteristics. In terms of the diagram you made for the preceding problem, describe the collection A ^ B and the collection A U B.
Give the number of people in each of these collections (these numbers are designated by the notation n ( A ^ B) and n(A U B) ). Refer
to the diagrams you have made.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
(A^B) contains 8 elements. All elements have both dark hair and bright eyes.
(AUB) = Total # of people in room-35 minus (A^B)- 8 or 27 people
confidence rating #$&*: Very confident
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q002. Continuing the preceding example, we let A' stand for the people who are not in the collection A, and we let B' stand
for the people who are not in the collection B. What are the characteristics of the people in A', and what characterizes people in B' ?
What are n(A ') and n(B '), the numbers of people in A' and B' ?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
A' is the collection of people who have bright eyes. These are the 7 people in B + A^B or 15 people
B' is the collection of people who have dark hair . These are the 12 people in A + A^B or 20 people
confidence rating #$&*: Fairly Confident. Not sure when to leave items in the intersection out of calculation.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q003. ( A U B ) ' stands for the everyone outside A U B, and ( A ^ B ) ' stands for everyone outside A ^ B. What
characterizes the people in each of these collections, and how many people are there in each?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION: AUB' is everyone who has neither dark hair nor bright eyes or 8 people
A^B' is everyone who has neither characteristic and everyone who has 1 of the characteristics or 27 people
confidence rating #$&*: Fairly Confident.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q004. How many people are in A ' U B ', and how could those people be characterized? Answer the same for A ' ^ B '.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
A'UB' = 8 people. They are the people outside A and outsidegoe
A'^B'= 27 people. They are the parts of A and B that is not AUB and A' and B'
confidence rating #$&*: Not really confident on this one
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
*********************************************
Question: `q005. Succinctly describe the relationships between ( A U B ) ', A ' U B ', (A ^ B) ' and A ' ^ B '.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
YOUR SOLUTION:
(AUB)' = A'^B'. This is the collection outside of (AUB)
(A^B)' = A'UB'. This is the collection outside of (A^B)
confidence rating #$&*: Very confident
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!#*&!
@& As indicated before I can't review this properly unless you include the entire document, including given solutions and your self-critiques on those problems on which you aren't completely confident.
It would be a good idea for you to insert your solutions into the full document, then self-critique in the prescribed manner.
At that point, knowing what you do and do not understand about the given solution, I can help clarify anything you migh be missing.*@