SOLUTION: Given the following sets: U = {2, 4, 5, 6, 9, 10, 12, 16} A = {4, 5, 10, 12} B = {2, 4, 9, 12, 16} Find: n (A U B) Do not list the elements. (I'm very confused on this prob

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Question 1203836: Given the following sets:
U = {2, 4, 5, 6, 9, 10, 12, 16} A = {4, 5, 10, 12}
B = {2, 4, 9, 12, 16}
Find:
n (A U B)
Do not list the elements.
(I'm very confused on this problem here)
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

U = {2, 4, 5, 6, 9, 10, 12, 16}
A = {4, 5, 10, 12}
B = {2, 4, 9, 12, 16}
Find:
n (A U B)
Do not list the elements.
A = {4, 5, 10, 12} => n(A)=4
B = {2, 4, 9, 12, 16} => n(B)=5
since we have two elements in both sets, we will count them ones in union, so
n (A U B)=7

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

The "n" refers to "number of"
n(A) = number of values inside set A
n(B) = number of values inside set B
etc

The frustrating thing about this type of set mathematics is the letter "U" stands for "universal set" and it also looks very similar to the "union symbol".

To avoid confusion, I'll say "union" when joining two sets rather than just stating the symbol.

An important set operation is set intersection.
This is where we find what two sets have in common.
For a venn diagram, the intersection is the overlapped area.

A = {4,5,10,12}
B = {2,4,9,12,16}
A intersect B = {4,12}
This is because both 4 and 12 are in sets A and B at the same time.
Draw out a venn diagram if needed.

Then, by the inclusion-exclusion principle, we can state the following
n(A union B) = n(A) + n(B) - n(A intersect B)
n(A union B) = 4 + 5 - 2
n(A union B) = 7
There are 7 elements inside set A union B
Those 7 items are found in either:

I know your teacher directly mentions "do not list elements" but I think listing things helps verify the answer.

I'll use color-coding to show how the sets union together.
A = {4,5,10,12}
B = {2,4,9,12,16}

A union B = {4,5,10,12} union {2,4,9,12,16}
A union B = {4,5,10,12     2,4,9,12,16}
A union B = {2,4,5,9,10,12,16}
This is where we basically glue together sets A and B. Toss out any duplicates.
Sort the values to make life a bit easier.

To remember what "set union" means, what you can do is think of a marriage as a union of two people's stuff when those two people get married.
The set {couch,fridge,tv,house} from the bride unions with the set {car,house,tv,fridge} of the groom to get {couch,tv,fridge,house,car}.
The duplicate items are tossed. Assume that the couple can afford one of each item only.


Anyways,
A union B = {2,4,5,9,10,12,16}
n(A union B) = number of elements in set A union B
n(A union B) = 7
We have confirmed the answer.


-------------------------------------------
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Answer: 7
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