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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 * ∩ *H* ∪ *P *

b) (*G* ∩ *P*) ’ ∪ *H *

c) *H* ’ ∩ (*G* ∪* P* )

d) (*P * ∪ *H * ∪ *G*) ’ ∩ (*G* ∩ *H*)

**Solution: **

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

a) *G * ∩ *H* ∪ *P *= {2} ∪ *P *← *G * ∩ *H = *{2}

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

b) (*G* ∩ *P*) ’ ∪ *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*) ’ ∩ (*G* ∩ *H*) = {9} ∩ (*G* ∩ *H*)

= {9} ∩ {2} = { }

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

Bringing the set operations together.

Operations with Sets

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)

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.