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Solving Universal Sets - A ∩ B

by Elizabeth
(WI)










































Intersection of two sets

     • The set of all the possible elements is called a universal set. It is usually denoted by the symbol “U”.

         U = universal set = {0,1,2,3,4,5,6,7,8,9}

         set A = {1,3,4,5,9}

         set B ={2,4,6,7,8}

     • What is A ∩ B (the intersection of set A and set B)?


I'm having trouble solving ------

Thank You!

Comments for Solving Universal Sets - A ∩ B

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Sep 06, 2012
Intersection of two sets
by: Staff


Answer:


The following diagram is a visual representation of the Universal Set “U” described in the problem statement.

U = universal set = {0,1,2,3,4,5,6,7,8,9}


Venn Diagram:  Universal Set “U” =  {0,1,2,3,4,5,6,7,8,9}





Set A is composed of some (but not all) of the numbers in the Universal Set “U”.

set A = {1,3,4,5,9}

Because of this relationship between the two sets, Set A is a called a proper subset (math symbol ⊂)of the universal set “U”.

Set A ⊂Universal Set “U”

Or

A ⊂ U


This is shown on the following Venn Diagram.


Venn Diagram:  set A = {1,3,4,5,9}





Set B is also composed of some (but not all) of the numbers in the Universal Set “U”.

set B ={2,4,6,7,8}

Set B is also a proper subset (math symbol ⊂)of the universal set “U”.

Set B ⊂Universal Set “U”

Or

B ⊂ U


This is shown on the following Venn Diagram.


Venn Diagram:  set B ={2,4,6,7,8}



Both sets A and B contain different elements (numbers), except for one common element: the number 4.

This is shown in the following Venn Diagram.


This common element (the number 4) is where set A and set B overlap.

The overlap is called the “intersection” (math symbol ∩) of set A and set B.

A ∩ B = {4}

Venn Diagram:  A ∩ B = {4}




Final Answer

     What is A ∩ B (the intersection of set A and set B)?

          A ∩ B = {4}




Thanks for writing.

Staff
www.solving-math-problems.com



Jun 13, 2016
solutuions to the following NEW
by: Anonymous

problems:

1. A'∩ C'
2. (A ∩ C')
3. (B' ∪ C)'
4. (A ∪ B ∪ C)
5. (A ∩ B ∩ C)'



please i need solutions

Jun 13, 2016
need solutions NEW
by: Anonymous FABROS

U={0,1,2,3,4,5,6,7,8,9}
A={1,2,3,4,5,7}
B={0,2,4,6,7,8}
C={1,3,4,8}

PROBLEMS:
1. A' ∩ C'
2. (A ∩ C')
3. (B' ∪ C)'
4. (A ∪ B ∪ C)
5. (A ∩ B ∩ C)'



PLEASE. I NEED ANSWERS

Dec 17, 2017
solve for a=b=c= NEW
by: Anonymous

​,   n left parenthesis Upper A intersect Upper B intersect Upper C right parenthesis equals 5n(A∩B∩C)=5​,   n left parenthesis Upper B intersect Upper C right parenthesis equals 9n(B∩C)=9​,   n left parenthesis Upper B minus Upper A right parenthesis equals 6n(B−A)=6​,   n left parenthesis Upper B union Upper C right parenthesis equals 22n(B∪C)=22​,   n left parenthesis Upper A intersect Upper C right parenthesis equals 8n(A∩C)=8​,   
n left parenthesis Upper A union Upper B union Upper C right parenthesis equals 27n(A∪B∪C)=27.

Aug 15, 2022
help pls NEW
by: Anonymous

x = {u,b,e}
y = {a,t,i,s}
x ∩ y = {?}

help pls this is im my assignment


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