Grade 9 Chapter 1: Sets

Step 1: Identify the even numbers less than 10:

Even numbers are divisible by 2. The numbers less than 10 are 1, 2, 3, ..., 9.

Even numbers: 2, 4, 6, 8.

Step 2: Write in roster form:

In roster form, list the elements in curly braces.

\( A = \{2, 4, 6, 8\} \).

Step 3: Write in set-builder form:

In set-builder form, describe the property of the elements.

\( A = \{ x \mid x \text{ is an even number and } 0 < x < 10 \} \).

Step 4: Therefore, the set in roster form is \( \{2, 4, 6, 8\} \), and in set-builder form is \( \{ x \mid x \text{ is an even number and } 0 < x < 10 \} \).

Step 1: List the elements of the set:

Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.

Numbers less than 5: 1, 2, 3, 4.

Prime numbers: 2, 3.

So, \( A = \{2, 3\} \).

Step 2: Determine the number of elements:

The set \( A = \{2, 3\} \) has 2 elements.

Step 3: Classify the set:

- Finite set: A set with a limited number of elements.

- Infinite set: A set with an unlimited number of elements.

- Empty set: A set with no elements.

- Singleton set: A set with exactly one element.

Since \( A \) has 2 elements, it is a finite set.

Step 4: Therefore, the set \( A = \{2, 3\} \) is a finite set.

Step 1: Understand the union operation:

The union of two sets \( A \) and \( B \), denoted \( A \cup B \), includes all elements that are in \( A \), in \( B \), or in both.

Step 2: List the elements of \( A \cup B \):

Elements in \( A = \{1, 2, 3\} \).

Elements in \( B = \{3, 4, 5\} \).

Combine all elements, removing duplicates: 1, 2, 3, 4, 5.

Step 3: Write the union:

\( A \cup B = \{1, 2, 3, 4, 5\} \).

Step 4: Therefore, the union of \( A \) and \( B \) is \( \{1, 2, 3, 4, 5\} \).

Step 1: Understand the intersection operation:

The intersection of two sets \( A \) and \( B \), denoted \( A \cap B \), includes all elements that are in both \( A \) and \( B \).

Step 2: List the elements of \( A \cap B \):

Elements in \( A = \{2, 4, 6\} \).

Elements in \( B = \{4, 6, 8\} \).

Common elements: 4, 6.

Step 3: Write the intersection:

\( A \cap B = \{4, 6\} \).

Step 4: Therefore, the intersection of \( A \) and \( B \) is \( \{4, 6\} \).

Step 1: Identify the elements in each set:

\( A = \{1, 2, 3, 4\} \).

\( B = \{3, 4, 5, 6\} \).

Step 2: Find the intersection \( A \cap B \):

Common elements in \( A \) and \( B \): 3, 4.

\( A \cap B = \{3, 4\} \).

Step 3: Elements in \( A \) only:

Elements in \( A \) but not in \( B \): 1, 2.

Step 4: Elements in \( B \) only:

Elements in \( B \) but not in \( A \): 5, 6.

Step 5: Draw the Venn diagram:

Draw two overlapping circles labeled \( A \) and \( B \).

Place 3, 4 in the overlapping section (\( A \cap B \)).

Place 1, 2 in the \( A \) circle (outside the overlap).

Place 5, 6 in the \( B \) circle (outside the overlap).