Chapter 2. De Morgan’s law and negation of complex propositions

When negating a compound proposition, simply adding ‘an’ or ‘not’ in front of the word is the way of the underdogs. Experts ‘flip’ the logical structure of the entire sentence through De Morgan’s Law. In particular, in public enterprise writing, negation is induced through the question “Which of the following is not true?”, so this rule is like a survival skill.

1. DeMorgan’s Core: Switch Strategy

When the negation sign (~) enters parentheses, two things change:

1. True/False of each element changes.
2. The connecting link connector (∧, ∨) switches.

2. Strategic understanding of the ‘or(∨)’ proposition

When you encounter the sentence “It is either A or B” in a public enterprise exam, you must think of the following three things at the same time. (This is the core of the 200,000 won lecture.)

1. At least one person: At least one of A and B is true. (both can be true)
2. 조건문 변환: ~A → B (A가 아니면 무조건 B여야 한다)
3. Remove declaration: What if A ∨ B is true but A is false? → B is unconditionally true.

3. Evolving problem solving (Step 5: De Morgan application)

Problem 4: When the proposition “I eat fruits and vegetables” is false, what is necessarily true?

1. I don’t eat fruit and I don’t eat vegetables.
2. If you don’t eat fruit, eat vegetables.
3. Don’t eat fruit or vegetables.
4. If you eat vegetables, don’t eat fruit.

4. Solving evolving problems (Step 6: Chain of complex negation)

Problem 5: If all of the following premises are true, which one is necessarily true?

• Premise 1: Either A passes or B passes.
• Premise 2: If A passes, B also passes.
• Premise 3: The bottle did not pass.

1. Student B did not pass.
2. Both A and B passed.
3. Student B passed.
4. Person A passed.

🚀 Insight from the 200,000 won lecture

In practice, De Morgan’s law itself does not appear alone, but is combined with declaration removal (A∨B, ~A ∴B) as in the above problem. When you see information that says “A or B,” always prepare for the “the moment it turns out that it’s not one of them, the other one is the culprit.”**

In the next supplementary lesson, you will learn how to solve difficult quizzes with insufficient information through reductio ad subjunctive law and number of cases.