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Set Theory: Combined Operations




 

Combined operations involve the intersection, union and complement of sets. Perform the operations within brackets first. Other operations are performed from left to right.

Related Topics: More Lessons on Sets

Example:

Given that U = {x : 1 ≤ x ≤ 10, x is an integer},

G = {x : x is a prime number},

H = {x : x is an even number},

P = {1, 2, 3, 4, 5}.

List the elements of:

a) G HP

b) (GP) ’ ∪ H

c) H ’ ∩ (G P )

d) (P H G) ’ ∩ (GH)

Solution:

G = {2, 3, 5, 7}, H = {2, 4, 6, 8, 10}

a) G HP = {2} ∪ P G H = {2}

= {1, 2, 3, 4, 5}

b) (GP) ’ ∪ H = {1, 4, 6, 7, 8, 9, 10} ∪ H

= {1, 2, 4, 6, 7, 8, 9, 10}

c) H ’ ∩ (G P ) = H ’ ∩ {1, 2, 3, 4, 5, 7}

= {1, 3, 5, 7}

d) (P H G) ’ ∩ (GH) = {9} ∩ (GH)

= {9} ∩ {2} = { }


The following video defines the set operations : Intersection, union and complement.



Bringing the set operations together.
Set Operations
1. Find the intersection of two sets
2. Find the union of two sets
3. Performs operations with sets
4. Determine sets involving set operations from a Venn Diagram
5. Understand the meaning of "and" and "or"
6. Use the formula for n(A ∪ B)


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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