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Logical reasoning exercise · ~60 sec a run · free

Deductive Logic

Two statements, one conclusion that must follow.

Session mode

Difficulty

Auto sets the level from your recent results: up when you are acing it, down when it is too hard.

How to play

  1. 1Accept both statements as true, even if they sound odd.
  2. 2Decide which conclusion is guaranteed by them.
  3. 3Pick the one that must follow; the others only might.
See a worked example

All Kralls are Brints. Some Dofts are Kralls. Which conclusion MUST be true? Draw it rather than argue it: a circle of Kralls sitting entirely inside a circle of Brints, and a circle of Dofts overlapping the Kralls somewhere. Now read off what the picture forces. The overlapping part is inside Kralls, and everything inside Kralls is inside Brints, so at least one Doft is a Brint: some Dofts are Brints. Try to draw a counter-example and you cannot. Then check what the picture does NOT force, because that is where the marks go: nothing stops some Dofts sitting outside the Krall circle, so all Dofts are Brints is not entailed, and nothing stops Brints extending well beyond Kralls, so all Brints are Dofts is not either. The two traps that catch almost everyone are turning an all statement around, and upgrading a some into an all. Must be true means true in every picture you can draw, not merely true in the first one.

Given two statements you must take as true, decide which conclusion is forced. Pure deduction with invented words, so only the logic counts.

About this test

What this test measures

This measures deductive reasoning and logical validity: following premises to a conclusion that must be true, without smuggling in assumptions. Procedures and system logic reward exactly this discipline.

How to improve your score

  • Take only what the premises actually state, never what seems likely from experience.
  • Sketch the relationships, a quick diagram or chain exposes a valid conclusion fast.
  • Beware reversed conditionals, if A then B does not mean if B then A.

Good to know

  • Draw the circles

    Sketch the groups as overlapping or separate circles. The words all, no and some translate straight into how the circles sit, which makes the forced conclusion visible.

  • Must follow, not might

    A conclusion holds only if it is true in every case where the statements are true. If you can picture one case where it fails, it does not follow, no matter how likely it seems.

Frequently asked questions

Why are the words made up?

Invented words stop real-world knowledge from biasing you. The answer depends only on the structure of the statements, which is exactly what the test measures.

What does 'must follow' mean?

A conclusion follows only if it is true in every case where both statements are true. If you can imagine a case where it is false, it does not follow.

Any tips?

Sketch the groups as overlapping or separate circles. 'All', 'No' and 'Some' translate cleanly into how the circles sit, which makes the valid conclusion obvious.

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