List the elements in each set. See Example 1. {a|a is an even integer greater than 8}

Verified step by step guidance

1. Understand the set notation: The set is defined as {a | a is an even integer greater than 8}, which means it includes all even integers that are strictly greater than 8.
2. Recall that even integers are integers divisible by 2, such as ..., 6, 8, 10, 12, 14, ...
3. Identify the smallest even integer greater than 8, which is 10.
4. List the elements starting from 10 and continuing with even integers: 10, 12, 14, 16, and so on.
5. Since the set is not bounded above, it contains all even integers greater than 8, so the list continues indefinitely.

Key Concepts

Set-builder Notation

Set-builder notation describes a set by specifying a property that its members must satisfy. It typically uses a variable and a condition, such as {a | condition on a}, meaning the set of all elements a that meet the given condition.

Even Integers

Even integers are whole numbers divisible by 2 without a remainder. Examples include ..., -4, -2, 0, 2, 4, 6, 8, etc. Recognizing even integers helps identify which numbers satisfy the condition in the set.

Inequalities and Number Sets

Inequalities like 'greater than 8' restrict the range of numbers considered. Understanding how to apply inequalities to integers allows listing all elements that meet both the parity and size conditions in the set.