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# BIOL 240: Microbiology 1
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# ECE 203: Probability
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# ECE 207: Signals and Systems
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# ECE 208: Discrete Math 2
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## Hilbert system rules
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**Axioms:**
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- $\vdash (A\implies (B\implies A))$
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- $\vdash (A\implies (B\implies C))\implies ((A\implies B)\implies (A\implies C))$
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- $\vdash (\neg B\implies\neg A)\implies (A\implies B))$
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**Inference (MP):**
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- $\frac{\vdash A, \vdash A\implies B}{\vdash B}$
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**Derived rules:**
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- Deduction: $\frac{U\cup \{A\}\vdash B}{U\vdash A\implies B}$
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- Contrapositive: $\frac{U\vdash \neg B\implies\neg A}{U\vdash A\implies B}$ (and vice versa)
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- Transitivity: $\frac{u\vdash A\implies B, U\vdash B\implies C}{U\vdash A\implies C}$
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- Exchange of antecedent: $\frac{U\vdash A\implies (B\implies C)}{U\vdash B\implies (A\implies C)}$
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- Double negation: $\frac{U\vdash \neg\neg A}{U\vdash A}$ (and vice versa)
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- Reductio ad absurdum: $\frac{U\vdash\neg A\implies false}{U\vdash A}$
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# ECE 224: Embedded
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# ECE 252: Concurrency
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- "ECE 250: DSA": 2a/ece250.md
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- "ECE 205: Advanced Calculus 1": 2a/ece205.md
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- "ECE 204: Numerical Methods": 2a/ece204.md
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- Computer Engineering 2B:
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- "ECE 208: Discrete Math 2": 2b/ece208.md
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- "ECE 207: Signals": 2b/ece207.md
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- "BIOL 240: Microbiology 1": 2b/biol240.md
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- "ECE 203: Probability": 2b/ece203.md
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- "ECE 224: Embedded": 2b/ece224.md
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- "ECE 252: Concurrency": 2b/ece252.md
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theme:
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name: material
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