Question

Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {History, Math, English, Drama},

 B = {Chemistry, Physics, French, English, Drama},

 and C = {Psychology, Math, French}.

 Find the following.

n[(A ∪ B) ∪ C]

Answer 1

The union $A ∪ B$ includes the elements which are in $A$ or in $B,$ or in both

$$A ∪ B=\{History, Math, English, Drama,$$

$$Chemistry, Physics, French\}$$

The union $(A ∪ B) ∪ C$ includes the elements which are in $A ∪ B$ or in $C,$ or in both

$$(A ∪ B) ∪ C=\{ History, Math, English,$$

$$Drama, Chemistry, Physics, French,$$

$$Psychology\}$$

The number of elements in $(A ∪ B) ∪ C$ is

$$n[(A ∪ B) ∪ C]=8$$