Disjoint Complement Symmetric Difference of Sets

In this class, We discuss Disjoint Complement Symmetric Difference of Sets.

The reader should have prior knowledge of the Venn diagram representation of sets. Click here.

Disjoint Sets: Two sets, X and Y, are said to be disjoint if no common elements exist between the sets.

Example:

A = {1, 2, 5}

B = {7, 8, 9}

The below diagram shows the disjoint sets.

Mutually disjoint sets:

A collection of sets is a disjoint collection if every pair of sets in the collection are disjoint.

The elements of a disjoint collection are called mutually disjoint.

Example:

A = {1, 2, 5}

B = {7, 8, 9}

C = {10, 11, 12}

Complement of a set:

Let U be a universal set.

For any set A: U – A is called a complement of set A.

Example:

Let U = Z+

A = {1, 3, 5, . . .}

A’ = U – A = {2, 4, 6, . . . }

Symmetric difference:

Let A B be two sets.

The symmetric difference between A and B is the set consisting of all the elements belonging to A or B but not both.

A + B = {x/(x ∈ A and x ∉ B) or (x ∈ B and x ∉ A)}

A + B = (A – B) U (B – A)

Example:

A = {1, 2, 5}

B = (2, 6}

A + B = (A – B) U (B – A)

A + B = {1,5,6}