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 for the representation of a set using bracket notation, specifically the result of subtracting one set from another in finite listed form. The first set contains natural numbers greater than 3, and the second set contains integers less than 5.
Answer
$$ \{ n \in \mathbb{N} | n \geq 5 \} $$
Answer for screen readers
$$ { n \in \mathbb{N} | n \geq 5 } $$
Steps to Solve
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Identify the first set
The first set is given by $ { n \in \mathbb{N} | n > 3 } $.
Natural numbers greater than 3 are:
$$ { 4, 5, 6, 7, 8, \ldots } $$ -
Identify the second set
The second set is given by $ { n \in \mathbb{Z} | n < 5 } $.
Integers less than 5 are:
$$ { \ldots, -3, -2, -1, 0, 1, 2, 3, 4 } $$ -
Perform the set subtraction
We need to subtract the second set from the first. This means we remove any elements of the second set from the first set.
The relevant elements from the first set (natural numbers greater than 3) are 4 and upwards.
We only need to subtract numbers from the second set that are also in the first. Thus the only number we will subtract is 4.
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List the result in bracket notation
After removing 4 from the first set, we have:
$$ { 5, 6, 7, 8, \ldots } $$
This can be represented in bracket notation as:
$$ { n \in \mathbb{N} | n \geq 5 } $$
This represents all natural numbers starting from 5.
$$ { n \in \mathbb{N} | n \geq 5 } $$
More Information
The subtraction of sets involves removing elements from one set that are present in another. In this case, we are removing the integer 4 from the natural numbers greater than 3, resulting in natural numbers starting from 5.
Tips
- Confusing natural numbers with integers. Remember that natural numbers are positive integers (1, 2, 3, ...), while integers include negative numbers.
- Forgetting to remove all applicable elements from the first set. It's crucial to examine which elements actually belong to both sets when performing the subtraction.
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