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Complement Of The Intersection Of Sets and Symmetric Difference




 
In these lessons, we will learn the complement of the intersection of sets, the symmetric difference of two sets and the symmetric difference of three sets.

The complement of the set XY is the set of elements that are members of the universal set U but not members of XY. It is denoted by (XY) ’.

The symmetric difference of two sets is the collection of elements which are members of either set but not both - in other words, the union of the sets excluding their intersection. Forming the symmetric difference of two sets is simple, but forming the symmetric difference of three sets is a bit trickier.

Related Topics: More Lessons on Sets

Example:

Suppose U = set of positive integers less than 10,

X = {1, 2, 5, 6, 7} and Y = {1, 3, 4, 5, 6, 8} .

a) Draw a Venn diagram to illustrate ( XY ) ’

b) Find ( XY ) ’

Solution:

a) First, fill in the elements for XY = {1, 5, 6}

Fill in the other elements for X and Y and for U

Shade the region outside XY to indicate (XY ) ’

b) We can see from the Venn diagram that

(XY ) ’ = {2, 3, 4, 7, 8, 9}

Or we find that XY = {1, 5, 6} and so

(XY ) ’ = {2, 3, 4, 7, 8, 9}




Symmetric Difference of two sets and three sets.
Symmetric Difference of Sets
Definition and properties of the symmetric difference of two sets.


 
Learn the difference of sets.

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You can use the free Mathway widget 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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