 |
|
|
 |
New Member
|
|
Sep 9, 2012, 07:55 AM
|
|
Finite Math help for free?
A and B are subsets of the universal set U. Given n(A')=23, n(B')=16, and n((A ∩ B) U (AUB)'))= 24, find (A∩B)
I know the answer, I just don't know how to get it without guessing and checking.
|
|
 |
Uber Member
|
|
Sep 9, 2012, 08:14 AM
|
|
What does (A ∩ B) mean?
|
|
 |
New Member
|
|
Sep 9, 2012, 08:26 AM
|
|
Sorry, n(A ∩ B)
|
|
 |
Uber Member
|
|
Sep 9, 2012, 08:27 AM
|
|
Um... yea, but I was trying to know if you really understand what each of the terms in "n((A ∩ B) U (A U B)')) = 24" mean.
|
|
 |
New Member
|
|
Sep 9, 2012, 09:05 AM
|
|
 Originally Posted by Unknown008
Um... yea, but I was trying to know if you really understand what each of the terms in "n((A ∩ B) U (A U B)')) = 24" mean.
The number of elements in the intersection of A and B or Not in A nor B is 24.
|
|
 |
Uber Member
|
|
Sep 9, 2012, 09:06 AM
|
|
Can you draw this on a Venn diagram, and on separate diagrams, the other information provided?
|
|
 |
New Member
|
|
Sep 9, 2012, 09:23 AM
|
|
 Originally Posted by Unknown008
Can you draw this on a Venn diagram, and on separate diagrams, the other information provided?
The space (sometimes an oval) between A and B would be counted (or shaded), and the area outside of A and B would be shaded. I can't post pictures online because I don't have a camera or scanner connected to my desktop.
|
|
 |
Uber Member
|
|
Sep 9, 2012, 10:11 AM
|
|
1. n((A ∩ B) U (A U B)')) = 24
2. n(A') = 23
3. n(B') = 16
Okay, can you try to do a relation about those?
|
|
 |
New Member
|
|
Sep 9, 2012, 10:37 AM
|
|
 Originally Posted by Unknown008
1. n((A ∩ B) U (A U B)')) = 24
2. n(A') = 23
3. n(B') = 16
Okay, can you try to do a relation about those?
Initially I was going to say that n((A ∩ B) U (A U B)'))-n(B')-n(A')=(A ∩ B), but that doesn't work, since it's negative and I'm subtracting the area outside A and B twice. Since I was able to guess and check the answer, I know that the sum of n(A') and n(B') minus n((A ∩ B) U (A U B)')) is what is outside of A and B. However, I'm sure that's just luck.
Short answer: No, I can't...
|
|
 |
Uber Member
|
|
Sep 9, 2012, 11:27 AM
|
|
Hmm, I think the easiest way for me would be to assign some variables to the different areas.
n((A U B)') = a
n(A ∩ B) = b
n(A ∩ B') = c
n(A' ∩ B) = d
The first picture says: a + b = 24
The second: a + d = 23
The third: a + c = 16
And you are asked to find b.
Well, I don't think that there is a single solution to this.
For instance, we can get:
b - d = 1
b - c = 8
d - c = 7
And get that:
8 < b <= 24
7 < d <= 23
0 <= a < 16
Taking b = 9:
a = 15
c = 1
d = 8
Taking b = 10;
a = 14
c = 2
d = 9
[... ]
Taking b = 24;
a = 0
c = 16
d = 23
Which are all valid possibilities.
|
|
Question Tools |
Search this Question |
|
|
Add your answer here.
Check out some similar questions!
Free finite math help?
[ 1 Answers ]
Assume that the playbook contains 10 passing plays and 12 running plays. The coach randomly selects 8 plays from the playbook.
What is the probability that the coach selects at least 3 passing plays and at least 2 running plays?
Finite math help for free?
[ 0 Answers ]
The Dispatch Tool Works spends $18000 to produce 110 parts achieving a marginal cost of $150 . Find the linear cost function
Finite math help free?
[ 1 Answers ]
The produce department at a grocery store makes fruit baskets of apples, bananas, and oranges. The cost for each apple is $.85, for each banana is $.20, and for each orange is $.76. Suppose each basket needs to have 18 pieces of fruit and costs $9 to make. How many apples, bananas, and oranges...
Finite math help free?
[ 1 Answers ]
A new type of poker called the razorback six has been created by your finite instructor. This game is similar to regular poker except each player receives 6 cards instead of the traditional 5. He has also invented a few new hands. Find the probability of obtaining the following 4 hands if you are...
Free help with finite math?
[ 1 Answers ]
E and F are events such that P(E) = 0.35, P(F) = 0.40, and P(E ∩ F) = 0.14.(a) Find P(F | E)and P(E ∪ F).(Round your answers to two decimal places.)
View more questions
Search
|