# Nathan Brunelle Department of Computer Science University of Virginia www.cs.virginia.edu/~njb2b/theory Theory of Computation CS3102 – Spring 2014 A tale.

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Nathan Brunelle Department of Computer Science University of Virginia www.cs.virginia.edu/~njb2b/theory Theory of Computation CS3102 – Spring 2014 A tale of computers, math, problem solving, life, love and tragic death

Today: Formal Logic Review of discrete math Notation will be used heavily Unambiguous All answers require argument Goals: Develop intuition Practice fluency Note: today we’ll be more formal than I expect on the problems

Propositional Logic

First Order Logic

First Order Logic Inference

First Order Logic

General Proof Guidelines No need to be super formal Shorter is always better! “A picture is worth 1000 words” Don’t try to surprise people Consider all corner cases

Set Theory

Notation: {}: Set notation {1, 2, 3} is a set {1, 2, 3, …} is the set of all positive whole numbers

Set Theory

Useful Sets

Problem: (1/4) + (1/4) 2 + (1/4) 3 + (1/4) 4 + … = ? Find a short, geometric, induction-free proof. 1 1

Problem: (1/8) + (1/8) 2 + (1/8) 3 + (1/8) 4 + …= ? Find a short, geometric, induction-free proof.

Binary Relations

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