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.

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)

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