All razors are blades and all blades are metals; which of the given conclusions about metals, razors and blades logically follows?

Introduction / Context:
This is a basic syllogism problem involving three sets: razors, blades and metals. You are given two universal statements and must determine which conclusion correctly describes the relationship among these sets.

Given Data / Assumptions:

• Statement 1: All razors are blades.
• Statement 2: All blades are metals.
• Conclusion 1: All metals are razors.
• Conclusion 2: Some metals are blades.

Concept / Approach:
The two statements can be read as a chain of subsets: razors ⊂ blades ⊂ metals. That is, every razor is a blade, and every blade is a metal. From this chain, we can deduce certain subset relations but must be careful not to reverse them. We test each conclusion against this structure.

Step-by-Step Solution:
Step 1: From all razors are blades and all blades are metals, we know every razor is also a metal. However, the set of metals can be much larger than the set of razors. Step 2: Conclusion 1 claims that all metals are razors. This would mean metals ⊂ razors, which reverses the actual subset direction and is not implied. Step 3: Conclusion 2 claims that some metals are blades. Since every blade is a metal and we assume blades exist, there is at least one item that is both a blade and a metal. Step 4: Therefore conclusion 2 is necessarily true whenever the statements hold.

Verification / Alternative check:
Construct a simple example. Let blades be the set {b1, b2} and razors be {b1}, with metals containing {b1, b2, m1}. All razors (b1) are blades, and both blades are metals. Clearly, some metals (b1 and b2) are blades. At the same time, not all metals are razors because m1 is a metal but not a razor. This confirms that conclusion 2 is correct and conclusion 1 is not.

Why Other Options Are Wrong:
Option A says all conclusions follow, which is wrong because conclusion 1 does not. Option B says neither conclusion follows, ignoring the direct fact that blades are metals. Option D selects only conclusion 1, which reverses the direction of the subset. Option E suggests an either or condition, but the situation here is clear: only conclusion 2 is supported.

Common Pitfalls:
Students sometimes confuse all A are B with all B are A, which is not logically equivalent. The direction of the all statement matters. Another pitfall is to forget that if all blades are metals, then at least some metals (those blades) must exist as long as blades are not an empty set.

Final Answer:
The correct evaluation is that only conclusion 2 follows from the given statements.