Career & communication · course 62 of 105

Logical Reasoning Tests: Does It Follow?

Answer the question under every logical reasoning test, does it follow? Syllogisms, if-then statements and their converse and contrapositive, ordering puzzles and number series.

4 modules

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Runs in Claude (claude.ai, the Claude apps or Claude Code) with your own Claude account. A course opens there as soon as your payment goes through; nothing is shipped.

Preview

What it teaches

The question under every logical reasoning test: does this follow? First the words logic tests use (premise, conclusion, valid, converse, inverse, contrapositive), quoted from Wikipedia. Then three kinds of question: syllogisms (statements built from All, Some or No: does the conclusion follow?), if-then statements (write the converse, the inverse or the contrapositive; does a conclusion follow from an if-then and one more fact?), and small drills you can solve with a pencil: ordering puzzles (five people, one answer) and number and letter series. The AI asks 3 questions, places you, shows a short card per module, then gives you one question at a time.

It is not a copy of any employer’s test, and it can’t tell you what yours will contain, allow, time or score.

How long

42 items. About 25-35 rounds for a confident student up to about 55-70 for a beginner, plus a 12-item final: 1-3 sessions (estimate, not timed with a real student). The tutor gives a one-line save code at the end of each session.

From the answer key · M1, row S2

Premises: All managers are employees. All engineers are employees. Conclusion: All managers are engineers. Does the conclusion follow?

Think first, then show the answer

AnswerDoes not follow

WhyCounter-world (only these things exist): something that is an employee and an engineer but not a manager, and something that is a manager and an employee but not an engineer. Every group has a member, both premises are true there, and the conclusion is false.

The wrong answer it catchesFollows → you read “All A are B” as “A and B are the same group”. Managers all sit inside the employees, and engineers all sit inside the employees, but the employees can include people who are neither.

Treat the premises as true, even where real life disagrees. “It is not required for a valid argument to have premises that are actually true”; the only question is whether the conclusion follows from them.
Follows means valid: “an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false”. In plain words: if you can picture one world where both premises are true and the conclusion is false, the conclusion does not follow.

The modules

4 modules, drilled one item at a time.

M0
The words
The words: premise, conclusion, valid, converse, inverse, contrapositive
M1
Syllogisms: does the conclusion follow?
Does the conclusion follow? Syllogisms built from All, Some and No
M2
If-then: converse, inverse, contrapositive, what follows
Write the converse, inverse or contrapositive of an if-then, and say what follows from it
M3
Ordering puzzles and sequences
Five-person ordering puzzles, and the next number or letter in a series

Before it teaches, it asks

1
What kind of test are you preparing for (a graduate scheme or job application, a school or college test, or just curious), and have you done logic puzzles before?
2
Premises: All cats are animals. Some animals are black. Conclusion: Some cats are black. Does the conclusion follow?
3
What is the contrapositive of “If it rains, then the match is cancelled.” Write it as an if-then sentence.

What’s exact, and what isn’t

Show

Straight from the course’s own notes.

Words and rules (M0 and the teach cards): Word-for-word quotes from 14 English Wikipedia pages (premise, syllogism, validity, converse, contraposition, inverse, affirming the consequent, denying the antecedent, modus ponens, modus tollens, arithmetic progression, geometric progression, Fibonacci sequence, English alphabet), read 2026-10-12. A script checks every quote on a saved copy of its page; it does not re-fetch the live pages, which can change. Each M0 answer is built from those quotes.
M1 syllogisms: Every key is computed. A script tries every way to fill three groups with up to 3 things and up to 4 things, with the groups allowed to be empty and not allowed to be, and a conclusion “follows” only if no way makes both premises true and the conclusion false. All four runs must agree for every item. That is deliberate: the Syllogism page says “Even some of these are sometimes considered to commit the existential fallacy, meaning they are invalid if they mention an empty category.” So the 10 items are ones whose answer does not depend on that argument, and the course does not teach it (it is listed as outside this course). In this course “Some” means at least one, and possibly all; the card says so.
M2 if-then: The converse, inverse and contrapositive are built by script from the parts of each statement, and truth tables confirm which of them always agree with the original. Follows / Does not follow items are checked over all four true/false combinations of the two parts. The course treats “If P, then Q” as the only thing known, and as one-way (the Converse page: “the truth of the converse is generally independent from that of the original statement”).
M3 puzzles and series: Each ordering puzzle is solved by trying all 120 orders of five people: exactly one fits, and every clue is needed. The clue wording (“ahead of” means anywhere earlier, “immediately” means the very next place) is this course’s own and is stated on the card. Each series fits one of four rule families in the checking script and the key is that rule’s next term; no script can prove that no other rule fits a short list of numbers, so the card names the three kinds the items use (add, multiply, sum of the two before) and the working shows the rule.
Honest limits: No employer’s test, no timing, no reading-passage questions (“true, false or cannot say”). The names and examples in the items are made up; premises are always to be treated as true, so no real-world fact is needed or taught. The tutor is an AI following the course’s instructions file; the keys are fixed by a script.
Not in it yet: Reading-passage (verbal) reasoning, truth tables and symbols, the named syllogism forms (Barbara and the rest), syllogisms with more than two premises, drawing the groups as diagrams, logic grids and circular seating, interleaved or picture series.