1. Let's start by stating the problem: We want to understand the basics of set theory suitable for grade 9 students in Ethiopia. 2. A set is a collection of distinct objects, called elements. For example, the set of vowels in the English alphabet is $A = \{a, e, i, o, u\}$. 3. Sets are usually denoted by capital letters, and elements are listed inside curly braces $\{\}$. 4. Important concepts include: - Membership: If an element $x$ is in set $A$, we write $x \in A$. - Subset: Set $A$ is a subset of $B$ if every element of $A$ is also in $B$, written $A \subseteq B$. - Union: The union of sets $A$ and $B$ is the set of elements in $A$ or $B$, written $A \cup B$. - Intersection: The intersection of $A$ and $B$ is the set of elements in both $A$ and $B$, written $A \cap B$. - Difference: The difference $A - B$ is the set of elements in $A$ but not in $B$. 5. Example: Let $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$. - $A \cup B = \{1, 2, 3, 4\}$ - $A \cap B = \{2, 3\}$ - $A - B = \{1\}$ 6. These concepts form the foundation of set theory and are essential for further study in mathematics. Final answer: Understanding sets, membership, subsets, union, intersection, and difference is key to mastering set theory at grade 9 level.