집합론 정리

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"집합론 정리"에 대한 내용입니다.
집합론 정리본을 제출하는 과제였습니다.

목차

Ⅰ. Elementary Logic
Ⅱ. The Concept of Sets
Ⅲ. Relations and Functions
Ⅳ. Denumerable Sets and Nondenumerable Sets
Ⅴ. Cardinal Numbers and Cardinal Arithmetic
Ⅵ. The Axiom of Choice and Some of Its Equivalent Forms
Ⅶ. Ordinal numbers and Ordinal Arithmetic

본문내용

7. PROOF OF VALIDITY

The formal proof of q ≔ the sequence of statements s.t. for each i, is a axiom or the proved theorem or a hypothesis or a statement derived from and for using the rules of inference, and .

"If he studies medicine, then he prepares to earn a good living.
If he studies the arts, then he prepares to live a good life.
If he prepares to earn a good living or he prepares to live a good life, then his college tuition is not wasted.
His college tuition is wasted.
Therefore, he studies neither medicine nor the arts."

It may be symbolized as:
H 1. M → E
H 2. A → L
H 3. (E∨L) → ～W
H 4. W
C. ∴ ～M∧～A
The formal proof of validity for the above argument :
1. M → E (Hyp.)
2. A → L (Hyp.)
3. (E∨L) → ～W (Hyp.)
4. W/∴ ～M∧～A (Hyp./Concl.)
5. ～(E∧L) 3, 4, M.T.
6. ～E∧～L 5, De. M.

참고 자료

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