Some notes are coins and no coin is a card; on that basis, which of the given conclusions about cards and notes logically follows?

Introduction / Context:
This is a classic syllogism problem involving three sets: notes, coins and cards. The statements describe how these sets overlap or do not overlap. You must examine two proposed conclusions and decide which one logically follows if the statements are taken as perfectly true.

Given Data / Assumptions:

• Statement I: Some notes are coins.
• Statement II: No coin is a card.
• Conclusion I: All cards can be notes.
• Conclusion II: Some notes are neither coins nor cards.
• The phrase can be in conclusion I expresses possibility, not certainty.

Concept / Approach:
We interpret the statements using Venn diagrams or set language. Some notes are coins means there is at least one element common to the sets notes and coins. No coin is a card means the set of coins and the set of cards do not overlap. A conclusion based on can be is valid if there exists at least one possible arrangement of the sets that satisfies the statements and also makes that conclusion true.

Step-by-Step Solution:
Step 1: Draw overlapping circles for notes and coins and mark an overlapping region to represent some notes are coins. Step 2: Draw the set of cards completely outside the set of coins, since no coin is a card. Step 3: Check conclusion I. It says all cards can be notes. This is possible if we place the circle for cards wholly inside the notes set but outside coins. This arrangement satisfies both statements and makes all cards notes. So conclusion I is logically possible. Step 4: Check conclusion II. It claims there are some notes that are neither coins nor cards. The statements do not force this. It is possible that the only notes that exist are exactly those that are also coins, leaving no notes in the region outside coins. Step 5: Therefore conclusion II is not guaranteed, while conclusion I is a valid possibility that follows from the statements.

Verification / Alternative check:
Build two different models. In model one, let the set of notes be larger than the set of coins, so there are notes outside coins. In model two, let the set of notes coincide exactly with the set of coins. Both models satisfy the statements, but in model two there are no notes outside coins or cards, so conclusion II fails. This proves that conclusion II does not necessarily follow. However, in each model it is still possible to position cards inside notes, so conclusion I remains logically possible under the statements.

Why Other Options Are Wrong:
Option B selects conclusion II, which is not forced. Option C claims that neither conclusion follows, but conclusion I does follow in the sense of possibility. Option D requires both conclusions to follow, which is too strong because conclusion II is not necessary. Option E suggests that at least one of them must follow without specifying which, but the question asks you to identify the exact conclusion that follows, which is only conclusion I.

Common Pitfalls:
One common error is to misinterpret can be as must be, or to assume that if some notes are coins then there must also be notes that are not coins. Another mistake is to forget that absence of information does not mean the opposite is true. Because the statements do not say anything about notes outside coins, you cannot force conclusion II.

Final Answer:
The correct choice is that only conclusion I follows from the given statements.