Set and Roster notation problem

Question

My name is Richard Botte. Please use my name when answering the questions and please answer all questions. Thank you.

 

Using the letters from your first and last name, create a universal set and write this in roster notation. Please note you must use your full university display name. For example, if your university display name is “Megan Ryan” but you go by Meg you must use all the letters in your display name of Megan Ryan.

Create two proper subsets from your universal set and write them in roster notation. The first should be labeled F and contain letters from your first name, the second L and contain letters from your last name.

 

Do the following and write your answers in roster notation:
1.Find the union of the sets.
2.Find the intersection of the sets.
3.Find the complement of each of the sets.
Note: All sets should be written in roster notation.

Answer 1

Rich,

 

Think of a roster as a line up card that the manager uses in a baseball game. He lists all the players. Some can have the same last name but they have to be distinguished by a different first name, middle initial, or nickname because they are different individuals.

 

In this problem, your players are the individual letters in your name, but in this set there is no repetition of any letter.  So your name may have 2 t's but only a single t will appear.  I'll now use CAP letters to make them more readable.

 

name = RICHARD BOTTE

Roster Set F = {A,C,D,H,I,R}  from your first name

Roster Set L = {B,E,O,T}  from your last name

Roster Set U = {A,B,C,D,E,H,I,O,R,T} from both your names creates the Universal set.

 

(1) F ∪ L = F or L = U  ,  the union of the two proper sets is the universal set

(2) F ∩ L = F and L = only the elements in both F & L = {∅}, the null set since no letter is common to both

(3) Complement of F = U less F = set L, since the intersection was a null set

     Complement of L = U less L = set F, since the intersection was a null set.