S10
Proof & Logic
If-Then → Proof
"If A implies B, and B implies C, then A implies C."
Philosophical Origin：Aristotle syllogism
Minimal Example
All squares are rectangles. All rectangles have 4 sides. Therefore all squares have 4 sides.
One-Line Rule
"Logic chains from premise to conclusion."
Common Misconception vs Correct Understanding
Proof is just checking examples.
Proof shows it is true for all cases.
🌱 Growth Steps (Natural Evolution)
1 / 5 步
1
Implication: If-then statements
✨ Starting Point: Growth begins here
如果你能 ↑ 那么你就能 ↓
2
Contrapositive: Equivalent form
如果你能 ↑ 那么你就能 ↓
3
Direct proof: Logical chain
如果你能 ↑ 那么你就能 ↓
4
Proof by contradiction: Assume opposite
如果你能 ↑ 那么你就能 ↓
5
Mathematical induction: Infinite cases
SAT Example Question
Question:
If x>3 and y>5, what is the minimum value of x+y?
Answer:
More than 8
Explanation:
x+y > 3+5 = 8
Practice Questions
5 questions with multiple solution methods
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