Korean Logic • Chapter 2 • 4 min read

Public Enterprise Korean Language Logic Ch2. De Morgan's Laws and Compound Propositions — Solving Confusing 'Negations' for Good

O
Oiyo Contributor
2/5

Chapter 2. De Morgan’s Laws and the Negation of Compound Propositions

When you negate a compound proposition, simply slapping “not” in front of a word is the amateur move. Experts use De Morgan’s laws to “flip” the logical structure of the whole sentence. Public-company aptitude tests (NCS) love to trigger negation through prompts like “Which of the following is NOT true?” — which makes this law a survival skill.

1. The core of De Morgan’s laws: the switch strategy

When a negation sign (~) pushes into a set of parentheses, two things change:

  1. The truth value of each element flips.
  2. The connective (∧, ∨) between them switches.
De Morgan's First Law (Negating AND)
~(A ∧ B) ≡ ~A ∨ ~B
'Not both' means 'at least one is false.'
De Morgan's Second Law (Negating OR)
~(A ∨ B) ≡ ~A ∧ ~B
'Not either one' means 'both are false.'

2. A strategic read on “or (∨)” propositions

When a public-enterprise exam gives you the sentence “A or B”, you should immediately think of all three of the following at once. (This is the heart of the premium course.)

  1. At least one: At least one of A and B is true (both being true is also fine).
  2. Convert to a conditional: ~A → B (if A is false, B has to be true).
  3. Eliminate a disjunct: If A ∨ B is true and A turns out to be false, then → B has to be true.

3. Evolving problem practice (Step 5: applying De Morgan’s laws)

Question 4: When the proposition “I eat both fruit and vegetables” is false, which of the following must be true?

  1. I eat neither fruit nor vegetables.
  2. If I don’t eat fruit, I eat vegetables.
  3. I don’t eat fruit, or I don’t eat vegetables.
  4. If I eat vegetables, I don’t eat fruit.

[Thought process]

  1. Symbolize: Fruit (A) ∧ Vegetables (B)
  2. Apply the negation: ~(A ∧ B) ≡ ~A ∨ ~B
  3. Interpretation: “I don’t eat fruit, OR I don’t eat vegetables.”

Correct answer: 3

4. Evolving problem practice (Step 6: chaining compound negations)

Question 5: Given that all of the following premises are true, which one must be true?

  • Premise 1: Either A passes or B passes.
  • Premise 2: If A passes, C also passes.
  • Premise 3: C did not pass.
  1. B did not pass.
  2. Both A and B passed.
  3. B passed.
  4. A passed.

[Step-by-step algorithm]

  1. Symbolize: (1) A ∨ B, (2) A → C, (3) ~C (confirmed!)
  2. Start reasoning:
    • Since ~C is confirmed (3), the contrapositive of premise 2 (~C → ~A) confirms A did not pass (~A).
    • Since “A” turned out to be false in premise 1 (A ∨ B), the “eliminate a disjunct” rule forces the remaining option, B, to be true (passed).
  3. Conclusion: B passed.

Correct answer: 3

🚀 Insight from the premium course

In practice, De Morgan’s laws rarely appear on their own — they’re usually paired with disjunct elimination (A∨B, ~A ∴ B), exactly like the problem above. Whenever you see an “A or B” statement, always be ready for the scenario: “the moment one of the two is ruled out, the other one is guilty.”

In the next lesson, we’ll use reductio ad absurdum (the method of assumption) and case splitting to solve high-difficulty puzzles that don’t give you enough confirmed information.

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.