In each of the questions below, two conclusions are provided followed by five sets of statements. Assume the conclusions are true even if they contradict common knowledge. Determine for which set(s) of statements the conclusions logically follow.

**Conclusions:**

I. All letter can be down is not a possibility.

II. No mark being button is a possibility.

**Statements:**

Question

In each of the questions below, two conclusions are provided followed by five sets of statements. Assume the conclusions are true even if they contradict common knowledge. Determine for which set(s) of statements the conclusions logically follow.

**Conclusions:**

I. All letter can be down is not a possibility.

II. No mark being button is a possibility.

**Statements:**

Accepted Answer

**Solution:**

1. **Analyze Conclusion I:** "All letter can be down is not a possibility."
   - This means it is impossible for all letters to be down.

2. **Analyze Conclusion II:** "No mark being button is a possibility."
   - This means it is possible that no mark is a button.

3. **Check each statement set:**

- (a) All down is mark, and all mark is button, so all down is button. Since no arrow is down and only a few letters are arrow, it does not support conclusion I because letters could be down through mark and button. Also, since all mark is button, conclusion II (no mark being button) is not possible.

- (b) Some letter is button, only a few button is down, all arrow is down, no mark is arrow. Here, some letters can be down, so conclusion I is not supported. Also, since some mark is not arrow but no direct relation to button, conclusion II is unclear.

- (c) Only a few arrow are button, no down is arrow, only mark is letter, some arrow is mark.
   - Since no down is arrow and only mark is letter, letters cannot be down (because down is not arrow and letters are marks). So, all letters being down is not possible, supporting conclusion I.
   - Also, since some arrow is mark but only a few arrow are button, it is possible that no mark is button, supporting conclusion II.

- (d) All arrow is down, no letter is arrow, all button is letter, some mark is not letter.
   - Since no letter is arrow and all arrow is down, letters cannot be down, supporting conclusion I.
   - But all button is letter and some mark is not letter, so mark being button is possible, contradicting conclusion II.

- (e) No letter is arrow, all down is button, all button is arrow, no mark is button.
   - Since all down is button and all button is arrow, down is arrow, but no letter is arrow, so letters cannot be down, supporting conclusion I.
   - No mark is button supports conclusion II.

4. However, conclusion I states "All letter can be down is not a possibility," meaning letters cannot all be down. Statement (c) clearly supports this.

5. Conclusion II states "No mark being button is a possibility," which is also supported by statement (c) because only a few arrows are buttons and some arrows are marks, so no mark being button is possible.

**Answer:** (c)

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