CCAT syllogisms: when it's True, False, or Uncertain

What CCAT syllogism questions look like

You get two statements you must accept as true, then a conclusion. Your job is to say whether the conclusion is True, False, or Uncertain based only on those two statements. Not on what is likely. Not on what you know about the world.

They come in two shapes. Group statements use all, some, and no: "Some readers are editors. All editors are researchers. Conclusion: some readers are researchers." If-then statements give a rule and a fact: "If a package is express, it gets a tracking code. This package has a tracking code. Conclusion: it is express."

Both reward the same habit: read only what is written, then test it.

True, False and Uncertain, defined

• True: the conclusion must hold in every situation the two statements allow. There is no way to make the statements true and the conclusion false.
• False: the conclusion cannot hold in any situation the statements allow. The statements contradict it.
• Uncertain: the statements allow at least one situation where the conclusion holds and at least one where it does not. You cannot tell.

The useful way to think about it: True and False are both certainties. Uncertain means the two statements do not settle the question either way. That is a real answer, not a shrug.

The two-picture method for all, some and no

Draw each group as a circle. "All A are B" puts circle A entirely inside circle B. "No A are B" keeps them apart. "Some A are B" means the circles overlap and at least one member sits in the overlap.

Then draw two pictures, not one. In the first, try to make the conclusion true while obeying both statements. In the second, try to make it false while obeying both statements.

• Only the first picture is possible: True.
• Only the second is possible: False.
• Both are possible: Uncertain.

With practice you do this in your head. These six patterns cover most of what you will see:

The last two are where people lose points. Two groups that both sit inside a third need not touch each other. Two "some" statements can be about different members of the middle group, so nothing links the outer groups.

If-then rules and the contrapositive

An if-then rule says: whenever the first part (the condition) holds, the second part (the result) holds. "If a badge is active, the door unlocks." It says nothing about what happens when the badge is not active.

Four facts can follow a rule like "If A, then B". Only two of them prove anything.

The second row is the one to drill. "If A, then B" always means "if not B, then not A". If the door did not unlock, the badge was not active. And if the conclusion states the opposite of something you can prove ("the badge is active"), the answer is False.

Two wordings to translate before you start. "A only if B" means "if A, then B". "A unless B" means "if not B, then A".

Common traps

• Affirming the result. "If it rains, the street is wet. The street is wet. So it rained." Uncertain: a street cleaner could have done it.
• Denying the condition. "If it rains, the street is wet. It did not rain. So the street is dry." Uncertain, for the same reason.
• Reversing an all-statement. "All editors are researchers" does not mean all researchers are editors.
• Reading "some" as "only some". "Some A are B" means at least one, and possibly all. It does not tell you that some A are not B. From "some readers are editors", the conclusion "some readers are not editors" is Uncertain.
• Using what you know. If the statements say all fish can fly, then for this question, all fish can fly. Judge the logic, not the facts.
• Missing a negation. Harder questions put the "not" inside the conclusion: "it is NOT the case that the badge is active." Work out what you can prove first, then compare it to the conclusion word by word.

When Uncertain is the right answer

Many test takers treat Uncertain as the answer you pick when you are unsure. That is backwards. Uncertain is a precise claim: the statements allow it both ways.

In our bank, Uncertain is the correct answer on 137 of the 314 deductive and if-then questions, more than True (108) or False (69). That is our bank's distribution, not a rule about the real test. The point is that you should expect to answer Uncertain often, and only after you have found both pictures.

A quick check: if you can describe one situation where the conclusion holds and one where it fails, and both obey the statements, the answer is Uncertain. If you can only find one, keep looking for the other for a few seconds, then commit.

Eight practice questions with worked answers

These come from our bank, at medium and hard difficulty: four group statements and four if-then rules, with two True, two False and four Uncertain answers. Pick an answer, then open the explanation.

Where syllogisms fit in the CCAT

Syllogisms are logic questions. In our simulator, each 50-question test has 6 logic questions spread across 5 logic families: deductive statements, if-then reasoning, ordering, overlapping groups, and letter sequences. That is our simulator's mix, built to match the format; Criteria does not publish a per-type breakdown. With about 18 seconds per question, a syllogism you can settle in ten seconds banks time for slower questions.

The other logic types are on the CCAT logic questions page. Math has its own subtypes; the number series guide and the word problems guide cover the two that take the most practice.

How to practice syllogisms

Use the tables above until you can call each pattern without drawing. Then drill both families together, because the habit is the same. In the app, a focus drill on deductive statements and if-then reasoning times every answer and explains every miss, and the AI coach points out which trap you keep falling for.

Then put them in context with a free CCAT practice test, where a syllogism sits between a word problem and a rotation and you have to switch modes fast. More question types are on the CCAT practice questions hub.