# Thread: Union & Intersection

1. ## Union & Intersection

Sorry not too sure where this should go but I am having trouble with some uni level maths and its on union and intersection so here I go;

(A [union] B [union] C)

the key is;

A = {1,2}

B = {3,4,2}

C = {5,2,3}

Any help is greatly appriecated, thanks.

2. Originally Posted by mack3506
Sorry not too sure where this should go but I am having trouble with some uni level maths and its on union and intersection so here I go;

(A [union] B [union] C)

the key is;

A = {1,2}

B = {3,4,2}

C = {5,2,3}

Any help is greatly appreciated, thanks.
When you take the union of the sets, you take all the terms and put them in one set (however, if there are more than one of the same term, you should only list it once.

In your case, $\displaystyle A\cup B\cup C=\{1,2,3,4,5\}$.

When you consider intersections, you look for terms that each set have in common.

Even though you didn't ask this, what set do you think $\displaystyle A\cap B\cap C$ would generate?

3. Would it be the same output as the other symbol?

4. Originally Posted by mack3506
Would it be the same output as the other symbol?
No. The union takes all the elements in the sets and puts them all together.

In the intersection case, you're looking for common elements between the sets.

For example, if $\displaystyle A=\{2,5,3\}$ and $\displaystyle B=\{4,3,1\}$, then $\displaystyle A\cap B=\{3\}$.

However, there are some cases when they don't share anything at all: If $\displaystyle A=\{3,2,6\}$ and $\displaystyle B=\{1,4,7\}$, then $\displaystyle A\cap B=\emptyset$. (where $\displaystyle \emptyset$ means the empty set)

From your question, note that

$\displaystyle A=\{1,{\color{red}2}\}$
$\displaystyle B=\{3,4,{\color{red}2}\}$
$\displaystyle C=\{5,{\color{red}2},3\}$

So what would $\displaystyle A\cap B\cap C$ be?

5. = {2}

6. Originally Posted by mack3506
= {2}
That's correct!

Does this seem to make a little more sense?

7. Well not really as I am looking at my previous questions and now they are not making any sense at all , the questions are ..... using the same key which is;

A = {1,2}
B = {3,4,2}
C = {5,2,3}

workout (my answers are in the {});

A u B = {1,2,3,4}
A u B u C = {2}
B n C = {3,2}

8. Originally Posted by mack3506
Well not really as I am looking at my previous questions and now they are not making any sense at all , the questions are ..... using the same key which is;

A = {1,2}
B = {3,4,2}
C = {5,2,3}

workout (my answers are in the {});

A u B = {1,2,3,4}
A u B u C = {2}
B n C = {3,2}
The one in red is incorrect. If it was A n B n C = {2}, then that would be correct.

$\displaystyle A\cup B\cup C=\{1,2,3,4\}\cup\{5,2,3\}=\{1,2,3,4,5\}$

The other two are correct.