Use bracket notation to give the set {n ∈ N|n > 3} − {n ∈ Z|n < 5} in a finite listed form.
Understand the Problem
The question is asking us to express the set of natural numbers greater than 3, subtracting the set of integers less than 5, using bracket notation. We will first identify the elements of each set, then perform the subtraction and list the resultant set in a finite manner.
Answer
The resultant set in bracket notation is $$ \{5, 6, 7, 8, 9, \ldots\} $$.
Answer for screen readers
The resultant set in bracket notation is $$ {5, 6, 7, 8, 9, \ldots} $$.
Steps to Solve
- Identify the Set of Natural Numbers Greater Than 3
The natural numbers greater than 3 are: $$ {4, 5, 6, 7, 8, 9, \ldots } $$
- Identify the Set of Integers Less Than 5
The integers less than 5 are: $$ {\ldots, -3, -2, -1, 0, 1, 2, 3, 4} $$
- Perform the Subtraction of Sets
To find the resultant set, we subtract the set of integers less than 5 from the set of natural numbers greater than 3.
This subtraction means we will remove all the elements of the second set from the first set. Thus, we perform: $$ {4, 5, 6, 7, 8, 9, \ldots} - { \ldots, -3, -2, -1, 0, 1, 2, 3, 4 } = {5, 6, 7, 8, 9, \ldots} $$
- Final Result in Bracket Notation
The resultant set of natural numbers greater than 3, after subtracting integers less than 5, is: $$ {5, 6, 7, 8, 9, \ldots} $$
The resultant set in bracket notation is $$ {5, 6, 7, 8, 9, \ldots} $$.
More Information
The resulting set reflects the natural numbers that are strictly greater than 4, effectively capturing all natural numbers starting from 5 onwards. This reflects an infinite set of values.
Tips
Common mistakes include:
- Confusing natural numbers with integers. Remember that natural numbers start from 1 and do not include negative numbers or zero.
- Failing to properly interpret the set subtraction. It's important to remove only the elements that are explicitly in the second set.
AI-generated content may contain errors. Please verify critical information
