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Chapter 6: Problem 3

Write the set in set-builder notation. $$ \\{3,4,5,6,7\\} $$

Short Answer

Expert verified
The given set can be written in set-builder notation as: \(\{x \mid x \in \mathbb{Z}, 3 \le x \le 7\}\).

Step by step solution

01

Identify the pattern of the set

We can observe that the given set is an arithmetic sequence with consecutive integers, starting from 3 and ending at 7.
02

Write the set in set-builder notation using appropriate properties

Since all the elements in the set are consecutive integers, we can use the property that all members of the set are greater than or equal to 3 and less than or equal to 7. Here \(x\) represents an element of the set. Using set-builder notation, we can write the given set as: \[ \{x \mid x \in \mathbb{Z}, 3 \le x \le 7\} \]

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