# 【数学】命題と論理式，その証明のチートシート

ex.

### の証明

How to prove

1. Find x so that P(x) is true.
2. Prove that Q(x) is true.

ex.

### の証明

How to prove

1. Let x be any element satisfying P(x).
2. Prove Q(x)

### 命題が偽であることの証明

Statement X.

• It is True if we prove X.
• It is False if we prove the negation

### の証明

• For "", P is hypothesis or assumption, Q is conclusioin.
• In order to prove "", we have to prove Q by using the assumption that P is True.

### 推論のルール

Let P, Q, R be statements.

### 背理法

Prove by proving is false (or have a contradiction)

### の証明

How to prove .

1. Let x be an element (satisfying conditions).
2. Find y, which usually depends on x, so that is true.
3. Prove P(x, y).

### の証明

1. Find x so that it true
2. Let y be an element
3. Prove P(x, y)