Chapter 3. Engine of Reasoning: Syllogism and Consequent Negation

Once you’ve learned how to symbolize conditionals, it’s time to connect the symbols to create a ‘Chain’. 80% of logic quizzes end when you connect the scattered premises into one long chain of arrows.

1. Hypothetical Syllogism

“If A → B and B → C, then A → C.” It seems so obvious, but in actual exam papers, B is hidden in various forms.

Key: Finding the medium, B.
Tip: If you can’t see B directly, take the treat (~B→~A) and try to guess the tail.

Syllogism (Chain Link)

(A → B) ∧ (B → C) ⇒ A → C

Creates a logical flow that follows each other.

2. Negation of the consequent (Modus Tollens) ★★★

This is the ‘cheat key’ that test takers miss the most. It is a powerful tool for denying causes when you know the conclusion is false.

Modus Tollens

(A → B) ∧ ~B ⇒ ~A

If the result (B) did not occur, it is certain that the cause (A) did not occur.

Beware of inversion errors: In “When it rains, the ground gets wet”, do not conclude that “It rained (A)” just because “The ground was wet (B)”! (Someone may have sprinkled water on it) You can say “it didn’t rain(~A)” only if “the ground wasn’t wet(~B)“.

3. Solving evolving problems (Step 7: Chaining)

Problem 6: If all of the following premises are true, which conclusion is necessarily true?

Premise 1: If you are sincere, you will succeed.

Premise 2: If you are not happy, you are not successful.

Premise 3: Cheolsu is sincere.

The retreat was successful, but I was not happy.
Cheolsu is happy.
The withdrawal was not successful.
If you succeed, you will definitely be happy.

[Thought Process: Chain Construction]

Step 1 (Symbolization):

(1) Sincerity → Success
(2) ~Happiness → ~Success

Step 2 (Taking Treatment):

Treatment of (2): Success → Happiness

Step 3 (Chaining):

Sincerity → Success → Happiness
In other words, sincerity → happiness

Step 4 (substituting facts):

Cheolsu is sincere (T).
Therefore, Cheolsu is happy (T).

Correct answer: 2

4. Solving evolving problems (Step 8: Backward reasoning)

Problem 7: What premises are necessary to derive the following conclusion?

Premise 1: If the weather is nice, we go on a picnic.

Premise 2: I feel good when I go on a picnic.

Conclusion: If you’re not in a good mood, you’re under bad weather.

If the weather is bad, don’t go on a picnic.
If you feel good, you go on a picnic.
The conclusion is already drawn without any additional premises.
I don’t feel good if I don’t go on a picnic.

[Thought Process]

Chain: nice weather → picnic feeling → good mood
Final chain: good weather → good mood
Confirmation of conclusion: The conclusion “~good mood → ~good weather” is the treatment of the final chain.
Therefore, the situation has already been perfectly logically derived.

Correct answer: 3

🚀 Insight from the 200,000 won lecture

As soon as true experts see the premise, they change the ‘treatment’ in their head frequently and quickly catch structures such as “A → B → C” or “A → B, ~C → ~B.” As you practice, get into the habit of drawing arrows next to sentences. Coding is the only way to achieve both speed and accuracy.

In the next enrichment lesson, we will conquer a quiz of a higher difficulty level through reductio ad and number of cases.

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