1. ## Counting Sets

Let A and B be sets in a universe,
with |A ∩ B| = 4
|A U B| = 7
Determine the number of subsets in A U B which contains A ∩ B.

My Solution:
|AUB| = |A| + |B| - |A∩B|
=3+4-4=3

|A∩B|=|A|+|B|-|AUB|
=3+4-3=4

4+3=7

However i think it contradicts the given |A U B| = 7 ,which what i compute = 3.

Also i dont understand what it means by Determine the number of subsets in A U B which contains A ∩ B?? dosent AUB contains A ∩ B arleady?Please enlighten me on how should i solve this question.. thanks

2. Originally Posted by hugo84
Let A and B be sets in a universe,
with |A ∩ B| = 4
|A U B| = 7
Determine the number of subsets in A U B which contains A ∩ B.

My Solution:
|AUB| = |A| + |B| - |A∩B|
=3+4-4=3

|A∩B|=|A|+|B|-|AUB|
=3+4-3=4

4+3=7

However i think it contradicts the given |A U B| = 7 ,which what i compute = 3.

Also i dont understand what it means by Determine the number of subsets in A U B which contains A ∩ B?? dosent AUB contains A ∩ B arleady?Please enlighten me on how should i solve this question.. thanks
The numbers are pretty small, and one way to approach this problem is simply to make two sets A and B that fit the description and see what you have.

A={1,2,3,4}
B={1,2,3,4,5,6,7}

In this case A U B = B, but the lack of generality won't make the result invalid.

How many subsets of B contain A?

So the elements 5, 6, and 7, each can either be or not be in the subset. That is 2^3 possibilities. So I think the answer is 8.

3. Originally Posted by hugo84
Let A and B be sets in a universe,
with |A ∩ B| = 4
|A U B| = 7
Determine the number of subsets in A U B which contains A ∩ B.

My Solution:
|AUB| = |A| + |B| - |A∩B|
=3+4-4=3

|A∩B|=|A|+|B|-|AUB|
=3+4-3=4

4+3=7

However i think it contradicts the given |A U B| = 7 ,which what i compute = 3.

Also i dont understand what it means by Determine the number of subsets in A U B which contains A ∩ B?? dosent AUB contains A ∩ B arleady?Please enlighten me on how should i solve this question.. thanks
Fear you have not understood the question well. Where are you given |A| and |B| that you have used?
Let me ask a similar (infact exactly same question). You are given a set of 7 elements.
1. How many subsets this set has?
2. How many subsets are there that contain 4 particular elements?

Can you ans the above?

4. thanks for the clarification, understood
To: aman_cc
Qn1:2^7
Qn2:2^4