Discrete Mathematics(II) Spring 2013 Lecture 4: Proposition, Connectives and Truth Tables 1 Overview In last lecture, we give a brief introduction to mathematical logic and then redefine order and tree which has minor differences with the structures presented in last semester In this lecture, we discuss sentential logic. Topics focus first on the syntax of proposition. Semantics would be discussed shallowly. And the Adequacy Theorem is a very important theore 2 Propositions What is a proposition? It is the base of proposition logic. We should define clearly the object discussed in our class. Rethinking about every day language, especially the English, we need define some elementary objects to construct some complicated one before starting to learn the language Let's consider the following statements: 1. I am a student 2.I am not a student 3. I am a student and I study computer science 4. I am a boy or I am a girl. 5. If i am a student, i have a class in a week 6. I am student if and only if I am a member of some university. They are the statements in our life. "I am a student"is just declarative. And"I am not a student just denies the former one However, we do not consider the statements like the following 1. Are you a student? 2. Sit down please. 3. What are you doing? They are interrogative, imperative, and interrogative sentences respectively. It is very different withe the sentences in previous examples. Why we do not handle the sentence like are you a student? " because it is not determined or it is not declarative. all these statements are not declarative We first define a propositional letter, which represents a statement and claims one thing. For example, I am a student"is a sentence. But "I am a boy or I am a girl" is hard to say because itDiscrete Mathematics (II) Spring 2013 Lecture 4: Proposition, Connectives and Truth Tables Lecturer: Yi Li 1 Overview In last lecture, we give a brief introduction to mathematical logic and then redefine order and tree, which has minor differences with the structures presented in last semester. In this lecture, we discuss sentential logic. Topics focus first on the syntax of proposition. Semantics would be discussed shallowly. And the Adequacy Theorem is a very important theorem. 2 Propositions What is a proposition? It is the base of proposition logic. We should define clearly the object discussed in our class. Rethinking about every day language, especially the English, we need define some elementary objects to construct some complicated one before starting to learn the language. Let’s consider the following statements: 1. I am a student. 2. I am not a student. 3. I am a student and I study computer science. 4. I am a boy or I am a girl. 5. If I am a student, I have a class in a week. 6. I am student if and only if I am a member of some university. They are the statements in our life. ”I am a student” is just declarative. And ”I am not a student” just denies the former one. However, we do not consider the statements like the following: 1. Are you a student? 2. Sit down please. 3. What are you doing? They are interrogative, imperative, and interrogative sentences respectively. It is very different withe the sentences in previous examples.Why we do not handle the sentence like ”are you a student?”. Because it is not determined or it is not declarative. All these statements are not declarative. We first define a propositional letter, which represents a statement and claims one thing. For example, ”I am a student” is a sentence. But ”I am a boy or I am a girl” is hard to say because it 1