M
=
{
y
∣
y
∈
N
and
398
<
y
≤
420
}

The set \( M \) is defined as the set of all natural numbers \( y \) such that \( 398 < y \leq 420 \). 

This means that \( M \) includes all natural numbers greater than 398 and less than or equal to 420. 

To express this set explicitly, we list all the natural numbers within this range:

\[
M = \{399, 400, 401, 402, \dots, 420\}
\]

Now, let's list all the elements:

\[
M = \{399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420\}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you represent the set \( M \) using interval notation?
2. What is the cardinality of the set \( M \)?
3. How would you represent the set \( M \) using set-builder notation for an arbitrary range \( a < y \leq b \)?
4. Can you describe how this set would change if \( y \) were required to be an even number?
5. What is the smallest number in set \( M \)?

**Tip:** When working with sets, always ensure that the conditions for set membership are clearly defined to avoid confusion.

Explore the set theory problem involving natural numbers between 398 and 420. Learn how to define and list these numbers explicitly. Suitable for Grades 6-8 students studying set theory and number theory.

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