Discrete Mathematics

Question

A.     Write the following sets using roster method and set builder notation.

a.        Set of all factors of 15

b.       Set of all solution of the equation 8x=0

c.        Set of all integer’s solution of 2x^2 = 8

Answer 1

Note, I can't find the symbol for "in" when an element is in a set on Wyzant's math symbols so I will just write "in."

a.

Roster method: {1,3,5,15}.

Set-Builder notation: {x in N | there exist q in N, qx=15}.

Note the N should be in Doublestrike or Blackboard font and "there exist" should be replaced with its mathematical notation, a backward capital E.

b.

Roster method: {0}.

Set-Builder notation: {x | 8x=0}.

c.

First solving for x, we have

1. 2x²=8
2. x²=4
3. x=+2, -2

Roster method: {-2, 2}.

Set-Builder notation: {x in Z | 2x²=8}.