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





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)





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