Question

All medicines are drugs.
All drugs are chemicals.
Therefore, all medicines are chemicals.
The above statement is:

• A. True
• B. False
• C. Cannot be determined
• D. None of the above

Hint:

Use Set Notation for Syllogisms:
If $A \subset B$ and $B \subset C$, then $A \subset C$ is ALWAYS true!
Visualizing concentric circles helps solve syllogisms instantly.

Answer 1

The Correct Option is A

Topic Explanation:
This question is based on categorical syllogism, a form of deductive reasoning where a conclusion is drawn from two given or assumed premises.
In logical deductions, if all elements of Set A belong to Set B, and all elements of Set B belong to Set C, then logically all elements of Set A must belong to Set C.

Step 1: Understanding the Question:
We are given two premises and a proposed conclusion, and we need to verify whether the deduction is logically valid and true.

Step 2: Key Formula or Approach:
Represent the statements using subset notation or Venn Diagrams:
- Premise 1: $\text{Medicines} \subseteq \text{Drugs}$
- Premise 2: $\text{Drugs} \subseteq \text{Chemicals}$
- Transitive Property of Subsets: If $A \subseteq B$ and $B \subseteq C$, then $A \subseteq C$.

Step 3: Detailed Explanation:

• Analysis of Premise 1: "All medicines are drugs." This places the entire set of 'Medicines' completely inside the circle of 'Drugs'.

• Analysis of Premise 2: "All drugs are chemicals." This places the entire set of 'Drugs' completely inside the circle of 'Chemicals'.

• Deductive Deduction: Since the entire set of 'Medicines' resides inside 'Drugs', and 'Drugs' is entirely contained inside 'Chemicals', 'Medicines' is fully contained within 'Chemicals'.

• Evaluating the Conclusion: "Therefore, all medicines are chemicals." This matches the transitive property ($\text{Medicines} \subseteq \text{Chemicals}$).

Step 4: Final Answer:
The argument follows a valid categorical syllogism of the form Barbara (AAA-1), rendering the conclusion completely true. Hence, Option (A) is correct.