Q.Statements:
I. Some pictures are beds.
II. All beds are trees. Conclusions:
I. Some pictures are trees.
II. At least some trees are beds. Give answer:
A - only conclusion I follows.
B - only conclusion II follows.
C - either conclusion I or II follows.
D - neither conclusion I nor II follows.
E - both conclusion I and II follow.

What is a Categorical Syllogism?

Imagine you're trying to convince a friend that your new phone is waterproof. You might say: "All phones with IP68 rating are waterproof. My phone has an IP68 rating. So, my phone is waterproof." That chain of reasoning — two statements that lead to a third — is a syllogism. When every statement is about categories (groups of things) and uses words like "all," "no," or "some," it's a categorical syllogism.

The idea is ancient — Aristotle formalised it over 2,000 years ago — but it's still the backbone of logical reasoning in exams like the CLAT, AILET, and many competitive tests. You're essentially checking whether a conclusion must follow from two given premises, based purely on the structure of the statements, not on what the words mean.

The Three Parts

Every categorical syllogism has exactly three statements and three terms:

• Major premise — a general statement (e.g., "All mammals are warm-blooded")
• Minor premise — a more specific statement (e.g., "All dogs are mammals")
• Conclusion — what follows (e.g., "Therefore, all dogs are warm-blooded")

The three terms are:

• Major term — the predicate of the conclusion (here, "warm-blooded")
• Minor term — the subject of the conclusion (here, "dogs")
• Middle term — appears in both premises but not in the conclusion (here, "mammals")

The middle term is the bridge. It connects the other two terms. If the bridge is solid, the conclusion holds.

The Four Standard Forms (Moods)

Each statement can be one of four types, based on quantity (all/some) and quality (affirmative/negative):

The letters A, E, I, O come from the Latin affirmo (I affirm) and nego (I deny). Every categorical syllogism is described by a three-letter code — the mood — like AAA, EIO, AII, etc.

The Rules of Validity

Not every three-statement chain is logical. A valid categorical syllogism must satisfy six rules. Break any one, and the argument is invalid — even if the conclusion happens to be true in real life.

1. Three terms only — no more, no less. If a term is used in two different senses, it's a fallacy of equivocation.
2. Middle term must be distributed at least once — "distributed" means the statement refers to every member of that category. In "All dogs are mammals," "dogs" is distributed; in "Some dogs are brown," "dogs" is not.
3. Any term distributed in the conclusion must be distributed in its premise — you can't conclude something about all of a category if your premise only talked about some of it.
4. No negative premises — two "no" or "not" statements give no logical connection.
5. If one premise is negative, the conclusion must be negative — and vice versa.
6. If both premises are particular (I or O), no conclusion follows — you need at least one universal premise. …