Korean Logic • Chapter 3 • 4 min read

Public Enterprise Korean Language Logic Ch3. The Engine of Inference — Syllogisms and Modus Tollens

O
Oiyo Contributor
3/5

Chapter 3. The Engine of Inference: Syllogisms and Modus Tollens

Now that you know how to symbolize conditionals, it’s time to link those symbols into a “chain.” 80% of logic puzzles are solved the moment you connect a scattering of premises into one long chain of arrows.

1. The hypothetical syllogism

“If A→B and B→C, then A→C.” It sounds obvious, but on the actual exam, B is disguised in all kinds of forms.

  • Key point: Find the middle term, B.
  • Tip: If B isn’t directly visible, take the contrapositive (~B→~A) and try matching up the tail ends.
Hypothetical Syllogism (Chaining)
(A → B) ∧ (B → C) ⇒ A → C
Creates an unbroken logical flow, one link leading to the next.

2. Modus Tollens (Denying the Consequent) ★★★

This is the “cheat code” test-takers miss most often. It’s a powerful tool for negating a cause once you know the conclusion is false.

Modus Tollens
(A → B) ∧ ~B ⇒ ~A
If the result (B) didn't happen, the cause (A) certainly didn't happen either.

Watch out for the fallacy of affirming the consequent: from “If it rains, the ground gets wet,” you cannot conclude “it rained (A)” just because “the ground is wet (B)”! (Someone could have hosed it down.) You can only say “it didn’t rain (~A)” when you know “the ground isn’t wet (~B).“

3. Evolving problem practice (Step 7: chaining it together)

Question 6: Given that all of the following premises are true, which conclusion must be true?

  • Premise 1: If you are sincere, you succeed.
  • Premise 2: If you are not happy, you have not succeeded.
  • Premise 3: Cheolsu is sincere.
  1. Cheolsu succeeded, but he is not happy.
  2. Cheolsu is happy.
  3. Cheolsu did not succeed.
  4. If you succeed, you are necessarily happy.

[Thought process: building the chain]

  1. Step 1 (symbolize):
    • (1) Sincere → Succeed
    • (2) ~Happy → ~Succeed
  2. Step 2 (take the contrapositive):
    • Contrapositive of (2): Succeed → Happy
  3. Step 3 (chain them together):
    • Sincere → Succeed → Happy
    • In other words, Sincere → Happy
  4. Step 4 (plug in the fact):
    • Cheolsu is sincere (T).
    • Therefore, Cheolsu is happy (T).

Correct answer: 2

4. Evolving problem practice (Step 8: reasoning backward)

Question 7: Which premise is needed to derive the following conclusion?

  • Premise 1: If the weather is nice, we go on a picnic.
  • Premise 2: If we go on a picnic, we’re in a good mood.
  • Conclusion: If we’re not in a good mood, the weather wasn’t nice.
  1. If the weather isn’t nice, we don’t go on a picnic.
  2. If we’re in a good mood, we went on a picnic.
  3. The conclusion already follows with no additional premise needed.
  4. If we don’t go on a picnic, we’re not in a good mood.

[Thought process]

  1. Chain: Nice weather → Picnic → Good mood
  2. Final chain: Nice weather → Good mood
  3. Check the conclusion: “~Good mood → ~Nice weather” is simply the contrapositive of the final chain.
  4. So the conclusion is already fully and validly derived, with nothing extra required.

Correct answer: 3

🚀 Insight from the premium course

True experts flip to the contrapositive in their head the instant they see a premise, and instantly spot structures like “A → B → C” or “A → B, ~C → ~B.” As you practice, get in the habit of drawing an arrow next to every sentence. Symbolization is the only way to gain both speed and accuracy at once.

In the next lesson, we’ll use reductio ad absurdum and case splitting to conquer an even harder tier of puzzles.

O

Oiyo

Editorial Desk

The OIYO editorial desk researches money, law, lifestyle, and self-understanding topics against primary sources and public statistics. Every piece carries source notes and is reviewed on a regular cycle for accuracy and usefulness.