A syllogism combines premises about groups to test a conclusion. You can solve many of these questions by tracking inclusion, overlap and exclusion rather than relying on the everyday meaning of the group names.

Follow a chain of inclusion

All glints are blue tokens. All blue tokens are stored upstairs. Therefore, all glints are stored upstairs.

Think of glints as a group inside blue tokens, which is inside upstairs items. The conclusion follows the chain. The converse—all upstairs items are glints—does not follow.

Combine an existing example with a general rule

Some lamps are portable. All portable objects in the room are tagged. Therefore, some lamps are tagged.

The first premise guarantees at least one lamp in the portable group. The second applies to that object, so the overlap with tagged objects follows. The conclusion does not require all lamps to be portable or tagged.

An overlap that is not guaranteed

All glints are blue. Some blue objects are heavy. Must some glints be heavy? No. The heavy blue objects could belong entirely outside the glint group.

This example shows why a shared middle category is not enough. You must know that the relevant members overlap, not merely that both groups relate to blue objects.

Be careful about existence

Under the usual formal interpretation, all A are B does not by itself establish that any A exist. A some statement does establish at least one example. Follow any special conventions explicitly stated in a particular question.

A practical solving method

Translate each statement into inclusion, exclusion or guaranteed overlap. Then test whether the conclusion adds a reverse relation or an unstated overlap. If uncertain, construct a small arrangement of imaginary objects satisfying every premise. A single arrangement where the conclusion fails proves it is not forced. This method works even when the categories are deliberately unfamiliar words.