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I dont know how to calculate the dash also did i calculate right the A U B

needs help

A=1,2,3,4

B=3,4,5,6

U=1,2,3,4,5,6,7,8,9

(AUB)'

(AUB)=1,2,3,4

needs help

A=1,2,3,4

B=3,4,5,6

U=1,2,3,4,5,6,7,8,9

(AUB)'

(AUB)=1,2,3,4

Here is a good starting point to learn union (set theory) (Wikipedia).

"The union of two sets A and B is the collection of points which are in A or in B (or in both)"

>> so (AUB)=1,2,3,4,5,6,7,8,9

No.

>> A=1,2,3,4

>> B=3,4,5,6

>> U=1,2,3,4,5,6,7,8,9

A consists of 4 elements.

B consists of 4 elements.

I take it that by U, you mean the Universe of elements that you are considering, of which A and B are subsets of the Universe. Is that your understanding also?

If the elements in A were distinct from the elements in B, then at most AUB would have 8 distinct elements. Do you see that? Somehow, your union of AUB has 9 elements, so you should immediately raise a flag that something is wrong. Here is an example of X and Y having mutually distinct elements, and their resultant union.

```
X Y
--------- ----------
1 2 3 4 5 6 7 8
--------- ----------
XUY (has only 8 elements)
--------------------------
1 2 3 4 5 6 7 8
--------------------------
```

Now, try to draw and post the sets A and B, and then draw the union of A and B.---------------- --------------

1 23 4 3 4 5 6

----------------- --------------

sorry A U B=1,2,3,4,5,6

NOW how to calculate (A U B)'

Then, please explain what in the definition are you having problems with.

>> calculate (A' U B')

Those are the problems. In order to solve set theory problems, you have to first start with definitions and work with them. So, look up the definitions and post them; and I'll try to help you understand them to work out the problem.

<==> not[(x belongs A) V (x belongs B)] Definition of U

<==> not(x belongs A) ^ not(x belongs B) De Morgan's law

<==> (x belongs A') ^ (x belongs B') Definition of '

<==> x belongs A' intersect B' Definition of intersection

Therefore the sets (A U B)' and A' intersect B' are equal

--------- ----------

1 2 3 4 5 6 7 8

--------- ----------

XUY (has only 8 elements)

--------------------------

1 2 3 4 5 6 7 8

--------------------------

Now, suppose U = {0 1 2 3 4 5 6 7 8 9 10 11}

>> Definition of ': x belongs to (X U Y)' <==> not(x belongs X U Y)

x belongs X U Y ==> x is an element in { 1 2 3 4 5 6 7 8 }

>> not(x belongs X U Y) means the elements, x, that do not belong to X U Y

So, in this example, x cannot be any of { 1 2 3 4 5 6 7 8 }.

So what is left in the universe, U = {0 1 2 3 4 5 6 7 8 9 10 11}, that is not in X U Y in this example?

>> Definition of U: not[(x belongs A) V (x belongs B)]

So, in your other notation, U = not( AUB ), which means that if x is an element of U, then x is not an element of A and x is not an element of B.

In your OP:

>> U=1,2,3,4,5,6,7,8,9

But here, U has elements that are in A as well as B

So, for clarication, could you double-check the definition of U, and, possibly, write down the text's written description of its meaning. I was originally taking U to be the Universe of all elements that you are concerned with.

B=3,4,5,6

union of A and B are the elements of A and B together in one set (1,2,3,4,5,6)

intersection are the common elemenets of A and B in one set (3,4)

That's true. In your notation:

A^B = {3,4}

From your title, it might appear that you are interested in the intersection. However, your question is related to the tick operation:

(A U B)'

Getting an answer in set theory is nice, but not as important as understanding the definitions and notation.

Take your conclusion, for example:

(A U B)' <==> x belongs A' intersect B' Definition of intersection

What is A' ? Here is a picture illustrating the complement of A (taken from http://en.wikipedia.org/wiki/Complement_(set_theory) ). The outer rectangle is the entire Universe, U; and the red color is the complement of A, A'.

What is B' ?

If you know A' and B', then you easily figure out A' ^ B'

However, you should also compute (A U B)' and verify that they are the same.

If you have problems getting the results identical, let us know where, and we will try to help.

=============

Rather than just deal with symbols, it is easier to visualize the sets in a diagram.

```
A=1,2,3,4
B=3,4,5,6
U=1,2,3,4,5,6,7,8,9
```

In below figure, you see three sets: U, A, and B. A and B intersect, where A^B = {3,4}

```
U-------------------\
| |
| A--------\ |
| | 1 2 | |
| | | |
| B-+--------+-\ |
| | | 3 4 | | |
| | \--------/ | |
| | | |
| | 5 6 | |
| | | |
| \------------/ |
| 7 8 9 |
\-------------------/
```

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That looks good.

>> (A U B)' = {1,2,3,4,5,6} - U

Should be:

(A U B)' = U - {1,2,3,4,5,6}

>> B' U - B

I think you mean:

B' = U - B