Axiom Schemata for F Axiom Schema 1 A ∨ A ⊃ A Axiom Schema 2 A ⊃ (B ∨ A) Axiom Schema 3 A ⊃ B ⊃ (C ∨ A ⊃ (B ∨ C)) Axiom Schema 4 ∀xA ⊃ Sxt A where t is a term free for the individual variable x in A Axiom Schema 5 ∀x(A ∨ B) ⊃ (A ∨ ∀xB) provided that x is not free in A

Where Are W e Doing in This Chapter? After modeling consumers' choice set and his preference (represented by utility functions), we now put them together and model how he/she makes optimal choice. In mathematical terms, this is constrained maximization problem; In economics, this is rational choice problem

ynamic order statistics OS-SELECT(i, S): returns the i th smallest element in the dynamic set S. OS-RANK(, S): returns the rank ofx E S in the sorted order of s s elements IDEA: Use a red-black tree for the set S, but keep subtree sizes in the nodes

Ch. 5 Hypothesis Testing The current framework of hypothesis testing is largely due to the work of Neyman and Pearson in the late 1920s, early 30s, complementing Fisher's work on estimation. As in estimation, we begin by postulating a statistical model but instead of seeking an estimator of 6 in e we consider the question whether

1. Define - in their own words a definition for linking in a sentence. It is a revision and therefore, easy for most of the students; 2. Compare – based on the understanding of the basic concept, compare different types of linking in connected speech;

The students will learn strong forms and weak forms in English. Objectives: Students will be able to: 1. Define - in their own words a definition for strong forms and weak forms in a sentence. It is a revision and therefore, easy for most of the students;

Chapter F12 Power notes Corporations: Income and Taxes, nts in Stocks Stockholders' Equity, Investm Learning Objectives 1. Corporate Income Taxes 2. Unusual Income Statement Items 3. Earnings Per Common Share 4. Reporting Stockholders'Equity 5. Comprehensive Income 6. Accounting for Investment in Stocks 7. Business Combinations 8. Financial Analysis and Interpretation

Subject: English Pronunciation for Communication Purpose: The students will learn stressed syllables & unstressed syllables in English. Objectives: Students will be able to: 1. Define - in their own words a definition for stressed syllables & unstressed syllables. It is a revision and therefore, easy for most of the students; 2. Compare – based on the understanding of the basic concept, compare stressed and unstressed syllables in words and sentences;

Date: Sept.16-20 Class: Classes 1, 2 & 3, Grade 2002 Subject: English Pronunciation for Communication Purpose: The students will learn some basic concepts in English pronunciation. We are going to learn something about syllables, stress and rhythm in English. At the same time, they will learn to say greetings and farewell with appropriate pronunciation and intonation in English

In addition to the 'pure vowels' (ones where the tongue positioning is fairly static) shown above there is also the set of vowel diphthongs. These are effectively long vowels during which the tongue moves to produce a definite change of quality during the sound. In phonetic transcription we usually use a pair of linked symbols for each diphthong - one indicating the quality of the sound at the start of the vowel, and the other indicating its quality as it ends. Examples of diphthongs are found in words like 'boy', 'hear', 'may', 'my