1. **State the problem:** Prove the argument is valid: "All mathematicians are logical." "Some scientists are mathematicians." Therefore, "Some scientists are logical." 2. **Analyze the premises:** - Premise 1: All mathematicians are logical means \(\forall x (M(x) \rightarrow L(x))\). - Premise 2: Some scientists are mathematicians means \(\exists x (S(x) \wedge M(x))\). 3. **Apply logical reasoning:** From Premise 1, every mathematician is logical. From Premise 2, there is at least one individual who is both a scientist and a mathematician. 4. **Conclusion:** Therefore, this individual is logical (by Premise 1) and a scientist (by Premise 2), so \(\exists x (S(x) \wedge L(x))\). 5. **Explain in learner-friendly terms:** Since all mathematicians are logical, anyone who is a mathematician must be logical. Since some scientists are mathematicians, there is at least one scientist who is also logical. Hence, the argument is valid because the conclusion necessarily follows from the premises.