# Set TheoryWatch

#1
Let A = {1,2,3} B = {2,3}

Using |AuB| = |A| + |B| - |AnB|

|AuB| = {1} + {4} - {2,3}
|AuB| =

Thats as far as I got, don't know what to do next. I know with numbers you can just add/subtract and you obtain your answer. Bit confused as to when you have elements of a set.
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12 years ago
#2
Let A = {1,2,3} B = {2,3}

(AuB) = A + B - (AnB)

(AuB)={1,2,3} + {2,3} - {2,3}

={1,2,3}
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#3
Sorry, I got the sets wrong. They're

Let A = {1,2,3} B = {2,3,4}
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12 years ago
#4
(Original post by A.I.)
Sorry, I got the sets wrong. They're

Let A = {1,2,3} B = {2,3,4}
Just apply the same principle but with different elements.
AuB is just the set of elements in A or in B.
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#5
(Original post by Gaz031)
Just apply the same principle but with different elements.
AuB is just the set of elements in A or in B.
So would my answer be {1,4}?
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12 years ago
#6
(Original post by A.I.)
So would my answer be {1,4}?
Nope, {1,4} would be the intersection of A and B.
The union of A and B, denoted AuB, can be defined as so it simply contains all the elements that are in A, together with all the elements in B (but only write each element once).
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#7
(Original post by Gaz031)
Nope, {1,4} would be the intersection of A and B.
The union of A and B, denoted AuB, can be defined as so it simply contains all the elements that are in A, together with all the elements in B (but only write each element once).
would it be {1,2,3,4}? I'm really confused. Could you just tell me how to work it out as in the above post and i'll understand it better that way.
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12 years ago
#8
(Original post by A.I.)
Sorry, I got the sets wrong. They're

Let A = {1,2,3} B = {2,3,4}
AuB= A + B - AnB

= {1,2,3} + {2,3,4} - {2,3}

= {1,2,2,3,3,4} - {2,3}

= {1,2,3,4}
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#9
(Original post by wacabac)
AuB= A + B - AnB

= {1,2,3} + {2,3,4} - {2,3}

= {1,2,2,3,3,4} - {2,3}

= {1,2,3,4}
makes a lot of sense now. thanks. sorry gaz, im a bit thick when it comes to sets!
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12 years ago
#10
ehm Sorry if I'm mistaken but doesn't |A| mean the number of elements of A (for finite sets)?

In that case

|AUB|=|A|+|B|-|AnB| is just saying (For A={1,2,3} ,B={2,3,4} } ) that

4= 3+3 -2

why are you ppl keep adding and subtracting sets?

even if u did... don't use + and -, the "correct" symbols are AUB and A\B. altho they don't mean exactly the same.

Edit: And what is {1,2,2,3,3,4}? Never knew that if two elements of a set are the same we are not allowed (obligated?) to write that ONE element only once}. Anw as I said, I might be mistaken
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12 years ago
#11
A.I. What are you actually looking for? The number of elements in AuB or the actual elements themselves?
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