1. Let's clarify the math topic requirement: The topic should serve as the foundation for all statements to maintain thematic coherence in the argument. 2. Primitive statements should relate to or be inspired by this math topic so that the argument stays relevant and meaningful. 3. Structuring the argument: - Start with defining three primitive propositions per compound statement that relate to the chosen math topic. - Each person makes two compound statements, each including three primitive propositions combined with logical connectives (∧, ∨, →). - Each person then states a conclusion derived from their premises. - Finally, construct truth tables for each argument to verify validity (whether the conclusion logically follows from the premises). Example using the topic "Properties of Integers" (Grade 9 CAPS): Person A's argument (Teacher 1): - Premises (compound statements): 1.1 "If an integer is even, then it is divisible by 2 (p)." ∧ "If an integer is divisible by 2, it is not odd (q)." ∧ "If an integer is even, then it is not odd (r)." Symbolically: $(p \to q) \land (q \to r) \land (p \to r)$ 1.2 "An integer 4 is even (s)." ∧ "If 4 is even, then 4 is divisible by 2 (t)." ∧ "If 4 is divisible by 2, then 4 is not odd (u)." Symbolically: $s \land (s \to t) \land (t \to u)$ - Conclusion: "Therefore, 4 is not odd (u)." Person B's argument (Teacher 2): - Premises (compound statements): 2.1 "If an integer is odd, then it is not divisible by 2 (a)." ∧ "If an integer is not divisible by 2, then it has remainder 1 when divided by 2 (b)." ∧ "If an integer is odd, then it has remainder 1 when divided by 2 (c)." Symbolically: $(a \to b) \land (b \to c) \land (a \to c)$ 2.2 "The integer 5 is odd (d)." ∧ "If 5 is odd, then 5 is not divisible by 2 (e)." ∧ "If 5 is not divisible by 2, then 5 has remainder 1 when divided by 2 (f)." Symbolically: $d \land (d \to e) \land (e \to f)$ - Conclusion: "Therefore, 5 has remainder 1 when divided by 2 (f)." Next steps would include constructing truth tables for each argument to check validity. These steps demonstrate structuring according to the topic and maintaining clarity.