2.3 Venn Diagrams and Set Operations

Question 1

Venn diagram

Answer 1

A useful technique for illustrating set relationships. The rectangle represents the universal set, and the circle represents the subsets.

Question 2

Disjoint

Answer 2

Mutually exclusive. Two separate circles (subsets) in the box (universal set). Can’t happen at the same time.

Question 3

Subsets

Answer 3

Circle (subset) inside another circle (subset).

Question 4

Equal sets

Answer 4

Two sets that have the same members. One circle (subset) in box (universal set).

Question 5

Overlapping sets

Answer 5

Traditional venn diagram in box.

Question 6

Complement 𝐴′ (also A^C, 𝐴~)

Answer 6

The set of all elements in the universal set that are not in another set. (Ex: U = {a, b, c, d, e} A = {a, c, e} thus A’ = {b, d}) In a venn diagram, complements are represented outside of the circles (subset).

Question 7

Intersection A ∩ 𝐵

Answer 7

The set containing all the elements common to both set A and set B.
∩ meaning “and” or “intersects”

Question 8

Union ∪

Answer 8

The set containing all the elements that are members of set A or set B (both sets)
∪ meaning “or” or “union”

Question 9

n(A∪B) = n(A) + n(B) - n(A∩B)

Answer 9

General addition rule

Question 10

Difference of two sets (A - B)

Answer 10

The set of elements that belong to set A but not set B. Subtract the intersection.

Question 11

Cartesian Product (A × B)

Answer 11

The set of all possible ordered pairs of the form. Multiplying.