All S are T. If some U are S, what can be concluded about Some U are T?

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Multiple Choice

All S are T. If some U are S, what can be concluded about Some U are T?

When one group is entirely inside another, any member of the first group is automatically a member of the second. Here, all S are inside T. If some U are in S, those particular U are also in T because S is a subset of T. Therefore, there exists at least one U that is in T, so some U are T. We can’t conclude that all U are T, since only some U overlap with S and other U might lie outside S. We also can’t determine that no U are T, or that some U are not T, from these statements alone—the information guarantees at least one U is in T, but says nothing definitive about every U.

When one group is entirely inside another, any member of the first group is automatically a member of the second. Here, all S are inside T. If some U are in S, those particular U are also in T because S is a subset of T. Therefore, there exists at least one U that is in T, so some U are T.

We can’t conclude that all U are T, since only some U overlap with S and other U might lie outside S. We also can’t determine that no U are T, or that some U are not T, from these statements alone—the information guarantees at least one U is in T, but says nothing definitive about every U.

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