Given none of the red items are blue, and some red items are large, which statement is necessarily true?

• A. Some blue items are large.
• B. No blue items are large.
• C. At least one large item is not blue.
• D. All blue items are red.

Answer: (D)

Disjoint categories matter here: red items and blue items do not overlap. Since some red items are large, there exists at least one item that is large and red. That item, being red, cannot be blue, so there is a large item that is not blue. This makes the statement about at least one large item not being blue necessarily true.

The other idea, that all blue items are red, would require there to be no blue items at all to be true, which isn’t guaranteed by the given information. So it isn’t necessarily true, whereas the not-blue-large conclusion is.