CS1502 Formal Methods in Computer Science Lecture Notes 9 Proofs Involving Conditionals Methods of Proof Want to prove P Q. Direct Method assume P deduce Q ...
Logical-Necessity TW-Necessity Logical Necessity TW-Necessity Not a tautology Not a TW-Necessity Not a Logical Necessity Not a tautology According to the book, ...
Tom Hanks is a good actor. After all, all rich actors are good actors, and Tom Hanks is a rich actor. Proof Rules Proof rules are used to construct proofs ...
Tautologies and Logical Truth. 2. Constructing a Truth Table. Write down sentence ... S is a tautology. Tautological. All rows in truth table. Consequence ...
Will help you understand proofs in math, science, theoretical CS. Content ... My office hours are T,TH 1:30-2:30 and by appointment just send mail to set up ...
Objects: Identifiers begins with lower case letter, then caps for other words in identifier, ... iHeight = iH; } // Box Constructor // class definition continues...
4 new proof rules _|_ Intro, _|_ Elim, ~Intro, ~Elim ... This is a given fact. Suppose that p is odd. We will show that this leads to a contradiction. ...
1. Formal Methods in Computer Science. CS1502. The Logic of Boolean Connectives ... problem with atomic sentences (before Boolean connectives are introduces) ...
Second step: Pigeon-hole Principle. As M processes string ... Pigeon-hole principle. If there are more birds than holes, then some hole has two or more birds. ...
Elim. To gain skills in constructing proofs using proof by cases as well as simple proof rules. ... Elim. Select the conjunct that you want / Intro. Combine ...
... girl. ( intro) Since d was an arbitrarily chosen boy, thus every boy likes some girl. 19 ... Every boy likes some girl or other. Let e be any boy in the domain. ...
Equivalence of NFAs and DFAs. Closure properties of regular languages. ... A Nondeterministic Finite Automaton (NFA) is a 5-tuple (Q, , ,q0,F) where ...
arguments, valid arguments, sound arguments. 3. Properties of and Relationships among sentences ... Definition: An argument is sound if. the argument is valid and ...
... you don't *need* any of the con rules. 3. 6 Fitch Proofs ... use only Intro/Elim rules ... basketball. Some teachers do not have time for basketball. 5 ...
'For every object x, x is small.' Put it in Aristotelian form. 'For every object x, if x is in the domain, x is small.' 15. Summary: All P's are Q's ...
Tautological equivalence: equivalent solely in virtue of the meaning of. the boolean connectives ... Tautological equivalence. Equivalence of wffs. Equivalence ...
To learn about notion of 'tautology' for quantified sentences, and its use to ... Tautologies and Quantification ... Tautology: True solely in virtue of the ...
xy| p |y| 0 i (i 0 xyiz L) Need to find negation of ... xy| p, and |y| 0, for all i 0, xyiz is in L ... A good string has 2 properties. It can be pumped. ...
Title: CS1502: Introduction to Programming II Last modified by: Iren&Plamen Created Date: 6/19/1999 12:21:50 AM Document presentation format: On-screen Show
Methods of attack: Boole. Show P is a tautological consequence of (P Q) ... Non-consequence. Show the following argument is invalid. Cube(a) Cube(b) (Cube(c) Cube(b) ...
Thus, C is small and in front of B. (/ Intro) ... We want to prove that x Q(x) ... to infer something, say Q, from it, and essentially eliminating or consuming the ...