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Syllogism questions: true, false or cannot tell

Two or three statements, then a conclusion: true, false or cannot tell? The logic is simple. The traps are what cost points, and there are only a handful of them.

Updated October 14, 2026 · by TimedPrep. The 9 examples are practice questions written by us; tap an answer to check yourself.

A syllogism question gives you statements to accept as true and asks whether a final statement follows. The third option goes by several names: "uncertain", "cannot tell", "cannot be determined" or "not certain". It always means the same thing: the statements allow it to be true and also allow it to be false.

Rule one, before any trap: accept the statements, however odd they sound, and ignore what you know about the real world. "All managers are pilots" is true for the length of the question.

The quickest method is a sketch: circles for groups, a line for orders, an arrow for if-then. If you can draw the situation two ways and the conclusion is true in one and false in the other, the answer is "cannot tell".

1. "All A are B" works one way only

"All welders are committee members" lets you move a welder into the committee. It does not let you move a committee member back into the welders: the committee may have other people in it. Reversing an "all" statement is the classic mistake on these questions, and it hides inside chains too: all A are B and all B are C says nothing about whether all C are A.

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. All team leads are committee members. Tariq is a team lead. Tariq is a committee member. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: A. Everyone in the first group is in the second, and Tariq is in the first group. The third statement is true. Fast method: a rule about a whole group lets you move a member of that group forward into the second group, never backward from the second group into the first.

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. All employees who work weekends are drivers on Route 7. All drivers on Route 7 are employees with a commercial license. All employees with a commercial license are employees who work weekends. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: C. Call the groups A = employees who work weekends, B = drivers on Route 7, C = employees with a commercial license. The chain only runs one way: A sits inside B, which sits inside C. C may contain members that are not A, or may not. The third statement is uncertain. Fast method: draw quick circles for the groups; only 'all' and 'no' statements pin a circle in place.

2. "Some" means at least one, possibly all

"Some A are B" says nothing about the rest of A. Two "some" statements never connect: the A's that are B's may be different people from the B's that are C's. When a conclusion rests only on "some" statements, the answer is "cannot tell". A "some" joined to an "all" does carry through: some A are B and all B are C, so some A are C.

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. ("Some" means at least one, possibly all.) Some members of the safety committee are part-time employees. Some part-time employees are interns. Some members of the safety committee are interns. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: C. Call the groups A = members of the safety committee, B = part-time employees, C = interns. Two 'some' statements never force a link: the B's that are A's may be different from the B's that are C's. The third statement is uncertain. Fast method: draw quick circles for the groups; only 'all' and 'no' statements pin a circle in place.

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. ("Some" means at least one, possibly all.) Some field technicians are employees based in the Tampa branch. All employees based in the Tampa branch are employees with a company vehicle. Some field technicians are employees with a company vehicle. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: A. Call the groups A = field technicians, B = employees based in the Tampa branch, C = employees with a company vehicle. The A's that are B's are also C's (because every B is a C), so at least some A are C. The third statement is true. Fast method: draw quick circles for the groups; only 'all' and 'no' statements pin a circle in place.

3. If-then runs forward, and backward only in the negative

"If the tank is full, the pump shuts off". Tank full: pump shuts off. Pump did not shut off: the tank was not full. But a pump that shut off, or a tank that was not full, tells you nothing more: the pump may shut off for another reason. Those two are the traps, and their answer is "cannot tell".

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. If the alarm sounds, then the line stops. The alarm sounded. The line did not stop. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: B. The 'if' part happened, so the result must follow, and the last statement denies it. The third statement is false. Fast method: an 'if-then' rule works forward (if happened, so then) and backward only in the negative (then did not happen, so if did not).

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. If the alarm sounds, then the line stops. The line stopped. The alarm sounded. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: C. The result can have other causes. The rule runs one way only (affirming the result proves nothing). The third statement is uncertain. Fast method: an 'if-then' rule works forward (if happened, so then) and backward only in the negative (then did not happen, so if did not).

4. Orders: link the names in one chain

Taller than, older than, earlier than: write the names on a line as you read. If two names are connected through a chain, you can compare them. If they never meet in a chain (both are taller than the same person, say), the answer is "cannot tell".

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. Kira is older than Pia. Alma is older than Kira. Alma is older than Pia. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: A. Put the names on a line from top to bottom: Alma > Kira > Pia fits the given statements, and every order that fits makes the last statement true. Fast method: sketch the names on a line and read the answer off the sketch.

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. Alma scored lower than Ravi. Jamal scored lower than Ravi. Alma scored lower than Jamal. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: C. Two different orders both fit the given statements: Ravi > Jamal > Alma and Ravi > Alma > Jamal (each written from top rank to bottom rank). The last statement is true in one and false in the other, so it is uncertain. Fast method: sketch the names on a line; if two names are never linked through a chain, you cannot rank them.

5. False needs a contradiction, not a doubt

Pick "false" only when the statements make the conclusion impossible. If it is merely not proven, that is "cannot tell". Ask two questions in order: is it forced? Is it impossible? If neither, it is uncertain.

Sample · Logic statements · by TimedPrep

Assume the first two statements are true. ("Some" means at least one, possibly all.) All employees with a locker are forklift operators. No forklift operators are union members. Some employees with a locker are union members. The third statement is:

  1. True
  2. False
  3. Uncertain

Answer: B. Call the groups A = employees with a locker, B = forklift operators, C = union members. Every A is a B and no B is a C, so no A can be a C. 'Some A are C' contradicts that. The third statement is false. Fast method: draw quick circles for the groups; only 'all' and 'no' statements pin a circle in place.

The timing rule

Give a two-statement question 10 to 15 seconds and a three-statement one up to 25. Sketch, do not reread: reading the same lines a third time is the sign to answer and move on. On the PI, wrong answers do not count against you, so never leave one blank; on the Wonderlic, mark your best choice and keep moving.

Now try them on the clock. The free general cognitive test mixes logic statements with the other common question types: 50 questions, 15 minutes, no sign-up. When the clock stops you see which types cost you points.

Start the free test

Tests that use these questions, each with its own free full-length test: Wonderlic · CCAT · PI Cognitive Assessment · Wonderlic SLE.

Common questions

What does "cannot tell" or "uncertain" mean in a syllogism question?

That the statements allow the conclusion to be true and also allow it to be false. If you can sketch the situation two ways with different results, choose it.

When is the answer false rather than cannot tell?

Only when the statements make the conclusion impossible. A conclusion that is merely not proven is "cannot tell".

Which tests have syllogism questions?

The Wonderlic and the Wonderlic SLE (true, false or not certain), the PI Cognitive Assessment (formal logic, three choices), the CCAT and many general aptitude tests.

More question types, one worked example each: the Wonderlic, CCAT and PI sample-question pages · all guides.