Question

In each of the questions below, two statements are given followed by two conclusions numbered I and II. Consider the two given statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions logically follow(s) from the statements.

Statements: No coin is a dollar. Red token is a coin.
Conclusions:
I. Red token is not a dollar.
II. Red token may not be a dollar.

• A. if only conclusion II follows
• B. if only conclusion I follows
• C. if either conclusion I or II follows
• D. if neither conclusion I nor II follows

Hint:

If red token is entirely inside coin, and coin has zero overlap with dollar, what must be true about red token and dollar?

Answer 1

The Correct Option is B

Statements: No coin is a dollar, so coins and dollars are completely separate groups with zero overlap. Red token is a coin, so every red token lies inside the coin group.

1. Conclusion I (Red token is not a dollar): Since every red token lies inside the coin group, and the coin group has no members in common with the dollar group at all, a red token simply cannot be a dollar. This holds in every possible diagram consistent with the two statements, so it is definitely true.
2. Conclusion II (Red token may not be a dollar): This is the weaker "possibility" version of the same idea. Once conclusion I has already established, with certainty, that a red token is never a dollar, this possibility statement adds nothing new and is not treated as a separately following conclusion, under the usual convention for these definite-versus-possibility conclusion pairs, where only one of the two can be marked as following.

So only conclusion I follows, which is option (B). $\boxed{\text{Only conclusion I follows}}$