Set difference

A difference of sets A and B is a set C that consists of the elements that belong to A and don’t belong to B.

Difference is represented by such diagram:

Denoted A - B

Difference consists of the domain with light shading.

A – B = {x │ x A and x B}.

Ex.: A = {0, 1, 2, 3, 4}, B = 0, 2, 4, 6}, A - B = {1, 3}, B - A = {4, 6}.

Properties of intersection of two sets:

B - A A - B

B - A = Ā B

The difference of two sets can be expressed by means of compliment and intersection of sets.

H/t: Draw a Venn diagram for sets:

U

(A - B) (A B)

H/t: Given a Venn diagram.

Write a formula for each

of the domains.

Subsets of the universal set together with operations for sets constitute a special type of algebra. It’s called set algebra.

Formulas of the set algebra transform sets into other sets.

Example of a formula of the set algebra:

(Ā B) C. It specifies a new set, consisting of elements of sets A, B and C.

Priority of operations: ¯, , -.