Mathematics of Set

Mathematics of Set

Postby nycmathguy » Sat Jul 03, 2021 12:07 pm

If A and B are sets, the intersection of A with B, denoted A[tex]\cap[/tex] B is the set consisting of elements that belong to both A and B. The union of A with B, denoted A [tex]\cup[/tex] B is the set consisting of elements that belong to either A or B,
or both.

A = {1, 3, 5, 8}

B = {3, 5, 7}

C = {2, 4, 6, 8}

Finding the Intersection and Union of Sets
Let and Find:

1. A [tex]\cap[/tex] B

2. A [tex]\cup[/tex] B

3. B [tex]\cap[/tex] (A [tex]\cup[/tex] C)

Let me see.

1. A [tex]\cap[/tex] B = the elements found in both sets.
A [tex]\cap[/tex] B = {3, 5}

2. A [tex]\cup[/tex] B = {1, 3, 5, 7, 8}

3. B [tex]\cap[/tex] (A [tex]\cup[/tex] C)

I first must find A [tex]\cup[/tex] C.

A [tex]\cup[/tex] C = {1, 2, 3, 4, 5, 6, 7, 8}

I now find B [tex]\cap[/tex] C.

B [tex]\cap[/tex] C = {3, 5, 7}

You say?
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Re: Mathematics of Set

Postby nathi123 » Sun Jul 04, 2021 9:44 am

B={3,5,7}; C={2,4,6,8}[tex]\Rightarrow B \cap C = O[/tex] (empty set )

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Re: Mathematics of Set

Postby nathi123 » Sun Jul 04, 2021 11:43 am

B [tex]\cap( A \cup C )[/tex] = { 3,5}
because A[tex]\cup C[/tex] = {1,2,3,4,5,6,8}

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Re: Mathematics of Set

Postby Guest » Tue Jul 20, 2021 1:23 pm

There is no 7 in either A or C so there is no 7 in $A\cup C$.
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