Complement of a set
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Complement of a set

The Set U = { a,b, c,d, e,f,} A= {a, c, e} B= { b, d , e, f,} C= { a,b,d,f] Find each specified set


1.(A U B) U C'
Upside down U for aub i couldn't do it on my keyboard but i am having problems with this question

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Complement of a set

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Jan 21, 2011
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starstarstarstarstar 		Universal Complement of a Set
by: Staff


The question:

U = {a, b, c, d, e, f}

A= {a, c, e}

B= {b, d, e, f,}

C= {a, b, d, f}

Find each specified set


(A U B) U C'

Upside down U for aub i couldn't do it on my keyboard but i am having problems with this question


The answer:

To type the following symbols on your keyboard, hold down the ALT key, type the code, then release the ALT key:

⊂, subset, 8834
⊃, superset, 8835
∈, element of a set, 8712
∩, intersection, 8745
∪, union, 8746
Ø, null set, 0216

As I understand it, this is what you intend your expression to be:

(A ∩ B) ∪ C'


Step 1: A ∩ B, set A intersection with set B

The intersection of A and B is a new set which contains the elements common to both A and B

A= {a, c, e}

B= {b, d, e, f,}

A ∩ B = {e}; e is the only element which appears in both set A and set B


Step 2: C'

C', set C followed by the prime symbol ' stands for the universal (or absolute) complement of set C. This means EVERYTHING in the universe which is NOT in set C.


C = {a, b, d, f}

C' = everything in the universe except for {a, b, d, f}

Your universal set, U

U = {a, b, c, d, e, f}

C' = {c, e}


Step 3: {e}∪ C', the union of {e} with C'

{e}∪ C'

The element e already appears in C'.

The union of e with C' is still C'.


{e}∪ {c, e} = {c, e}



The final answer is:

(A ∩ B) ∪ C' = C'

(A ∩ B) ∪ C' = {c, e}




Thanks for writing.


Staff
www.solving-math-problems.com


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