Sets and Operations on Sets

Operations on Sets

Union, Intersection, Difference, Complement

Union of Sets

union => combining

For two given sets A and B, A∪B (read as A union B) is the set of distinct elements that belong to set A and set B or both.

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Union of Sets

Example

Consider the following sets:

Given

A = {1,2,3,4} B = {a,b,c};

Then,

A∪B = {1,2,3,4,a,b,c}

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Multiple Choice

If Set A = {L,E,B,R,O,N} and Set B = {J,A,M,E,S}, what is A ⋃ B?

• {L,E,B,R,O,N,J,A,M,E,S}

• {L,E,B,R,O,N,J,A,M,S}

• {T,H,E,K,I,N,G}

• { }

Multiple Choice

Given: A = {a, e, i, o, u}, and B = {a, b, c, d, e}

      Find: A ∪B. 

              

• A ∪B ={a, e, i, o, u, c, b}

• A ∪B = {a, b, c, d, e, u} 

• A ∪B ={a, e, i, o, u, b, c, d} 

• A ∪B ={a, e, i, o, u, b, c, d, b, c, d}

Intersection of Sets

Intersection => common

For two given sets A and B, A∩B (read as A intersection B) is the set of common elements that belong to both set A and B.

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​∩

Intersection of Sets

Example

Consider the following sets:

Given

A = {1,2,3,4} B = {2,4,6,8};

Then,

A∩B = {2,4}

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Multiple Choice

Given: A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6} and C = {1, 3, 5}

        Find: A ∩ C. 

              

• A ∪C = {1, 2, 3}

• A ∩C = {1, 3, 5} 

• A ⊃C = {1, 3, 5

• A ∩C = {2, 4, 6}

Multiple Choice

A = {2, 3, 4, 5, 6} and B = {4, 5, 6, 7}.

What is A∩B ?

• {2, 3, 4, 5, 6, 7}

• {4, 5, 6, 7}

• {4, 5, 6}

• { }

Difference between

Sets

difference=> present in A but not in B

The set operation difference between sets implies subtracting the elements from a set which is similar to the concept of the difference between numbers. The difference between sets A and set B denoted as A − B lists all the elements that are in set A but not in set B.

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Difference between

Sets

Example

Consider the following sets:

Given

A = {1,2,3,4} B = {2,4,6,8};

Then,

A-B = {1,3}

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Multiple Choice

U = { a, c, d, e, i } M = { a, e, i } N = { i, c, e } find M – N

• { a }

• { c }

• { i, e }

• { c, e }

Multiple Choice

U = { a, c, d, e, i } M = { a, e, i } N = { i, c, e } find N – M

• { a, e, i }

• { a, e }

• { a, c, d, e, i }

• { c}

Complement of a Set

complement=> present in U but not in A

The complement of a set A denoted as A′ or A^c (read as A complement) is defined as the set of all the elements in the given universal set(U) that are not present in set A.

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Complement of a Set

Example

Consider the following sets:

Given

U = {1,2,3,4,5} A = {2,3};

Then,

A' = {1,4,5}

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Multiple Choice

Given: U = {1, 2, 3, 4, 5}, and A = {1, 3, 5}

      Find: A’.

              }                                                                       

          

• A' = {1, 3, 5} 

•   A' = {1, 3} 

• A' = {2, 4

•    A' = {1, 5}

Multiple Choice

Given Universal set is U = set of real numbers and a set A = set of rational numbers then A' is

• Set of Natural Numbers

• Set of Real Numbers

• Set of fractions

• Set of irrational numbers

Practice Questions

Try !!!

Multiple Choice

Given the sets A = {2, 3, 4, 5} and B = {2, 4, 5, 6} What is $$A\cup B$$  ?

• {2, 4, 5}

• {2, 3, 4, 5, 6}

• {3}

• {6}

Multiple Choice

Given the sets A = {a, b, c, d, e} and B = {a, c, d, f} What is $$A\ \cap\ B$$  ?

• {a, c, d}

• {a, b, c,d e, f}

• {b, e}

• {f}

Multiple Choice

Given the sets U = {a, b, c, d, e, f, g, h, i, j} A = {a, c, e, g, i} and B = {b, c, d, e, f} What is  $$B'$$  ?

• {a, b, c, d, e, f, g, i}

• {b, d, f, h}

• {a, g, h, i, j}

• {c, e}

Multiple Choice

The Universal Set = { -4, -3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.

What is the complement of A?

• {-4, -3, -2, -1, 0, 1, 2, 3}

• {-3, -2, -1, 1, 2, 3}

• {-4, -3, -2, -1, 1, 2, 3, 4}

• {-4, -3, -2, -1, 1, 2, 3}

Multiple Choice

Given the sets A = {2, 4, 6, 8} and B = {3, 4, 5, 6, 7} What is $$B\ -\ A$$  ?

• {2, 3, 4, 5, 6, 7, 8}

• {4, 6}

• {8}

• {3, 5, 7}

Multiple Choice

Which of the following represents the shaded region?

• A union B

• A intersect B

• A ⊂ B

• B ⊂ A

Multiple Choice

If A = {1, 2, 3, 4, 5, 6}, B = {1, 2, 3, 5, 7, 9} and C = {3, 5, 6, 7, 8, 9}, what is (A ⋃ B) ⋂ C?

• {3, 4, 5, 6, 7, 9}

• {3, 4, 5, 6, 7, 8, 9}

• {3, 5, 6, 7, 9}

• { }

Multiple Choice

What operation is being shown by the shaded region?

• $$A-B$$  

• $$A'$$  

• $$A\cup B$$  

• $$A\cap B$$  

Multiple Choice

What operation is being shown by the shaded region?

• $$A\ -\ B$$  

• $$B'$$   

• $$A\cup B$$  

• $$A\cap B$$  

Multiple Choice

What is U = ?

• {6, 14, 20}

• {2, 4, 8, 10, 12, 16, 18}

• {2, 4, 6, 8, 10, 12, 14, 16, 20}

• {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

Multiple Choice

The Venn diagram for  $$A\cup B$$  is represented in green as

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

Multiple Choice

 If A = {1, 2, 3}, B = {3, 4, 5}, C = {5, 6, 7}, find A U B U C.

                                                    

             

• {1, 2, 3, 4, 5, 6, 7}

•   {1, 2, 3, 4, 5, 6, 7, 8} 

•   {1, 2, 3, 3, 4, 5, 5, 6, 7}

Multiple Choice

If A= {10, 20, 30, 40}, B = {20, 40, 60} and C = {10, 20, 40, 60, 80},

      find A Ո B Ո C.

                                                          

           

• {10,20, 30...}

• {20, 40, 60} 

• {20, 40}