Chapter 15 Logic Name Date Objective: Students will use

... The negation of proposition p is written as ¬p. Truth values are T for true and F for false. Proportion p p ...

... The negation of proposition p is written as ¬p. Truth values are T for true and F for false. Proportion p p ...

KNOWLEDGE

... some kind which ‘exists’ in the world. One objection is that it is the meaning of statements or beliefs which count, and this is what a proposition (p) is. Propositions rather than beliefs carry truth or falsity. I should say “p is true and I believe it” rather than “I believe p”. ...

... some kind which ‘exists’ in the world. One objection is that it is the meaning of statements or beliefs which count, and this is what a proposition (p) is. Propositions rather than beliefs carry truth or falsity. I should say “p is true and I believe it” rather than “I believe p”. ...

Philosophy of Language: Wittgenstein

... proposition is just to refer to an object. Russell, however, denies Frege’s claim that all singular terms are names. Rather, some singular terms are definite descriptions. Examples of definite descriptions are “the morning star” and “the evening star”. A proposition containing a definite description ...

... proposition is just to refer to an object. Russell, however, denies Frege’s claim that all singular terms are names. Rather, some singular terms are definite descriptions. Examples of definite descriptions are “the morning star” and “the evening star”. A proposition containing a definite description ...

Lecture_ai_3 - WordPress.com

... Types of Propositional Calculus • Atomic Proposition single proposition • Molecular (Complex)Proposition combines two or more propositions ...

... Types of Propositional Calculus • Atomic Proposition single proposition • Molecular (Complex)Proposition combines two or more propositions ...

Critical Terminology for Theory of Knowledge

... Analytic/synthetic: A proposition is analytic if and only if its truth value is guaranteed by the meanings of its terms; it is synthetic if its truth value is not guaranteed by the meaning of its terms. For example, All bachelors are unmarried is an analytic truth, All squares have five sides is an ...

... Analytic/synthetic: A proposition is analytic if and only if its truth value is guaranteed by the meanings of its terms; it is synthetic if its truth value is not guaranteed by the meaning of its terms. For example, All bachelors are unmarried is an analytic truth, All squares have five sides is an ...

Document

... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...

... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...

CHAPTER 0: WELCOME TO MATHEMATICS A Preface of Logic

... is being defined and italics to emphasize text for other reasons. For example, we will often use italics to emphasize terms that have not yet been defined. These terms may be undefinable, defined later in the notes, or you may need to look elsewhere for their definition. We use the term theorem in r ...

... is being defined and italics to emphasize text for other reasons. For example, we will often use italics to emphasize terms that have not yet been defined. These terms may be undefinable, defined later in the notes, or you may need to look elsewhere for their definition. We use the term theorem in r ...

Chapter 1 - National Taiwan University

... 1.2. A Famous Problem in Computer Science. In Example 2, we show how to use propositional logic to write system speciﬁcations. Additionally, we mentioned that system speciﬁcations should be consistent. That is, we should be able to assign truth values to propositions such that all requirements are s ...

... 1.2. A Famous Problem in Computer Science. In Example 2, we show how to use propositional logic to write system speciﬁcations. Additionally, we mentioned that system speciﬁcations should be consistent. That is, we should be able to assign truth values to propositions such that all requirements are s ...

Horseshoe and Turnstiles

... that is, if φ’s truth is not dependent on any other proposition(s). It is always true. We can express this as, (2) ⊧ φ. In this case, φ is also sometimes called a ‘logical truth’. More controversially, we could say that (2) says that φ is an axiom or a self-evident truth. Now, (3) Γ ⊧ φ iff there is ...

... that is, if φ’s truth is not dependent on any other proposition(s). It is always true. We can express this as, (2) ⊧ φ. In this case, φ is also sometimes called a ‘logical truth’. More controversially, we could say that (2) says that φ is an axiom or a self-evident truth. Now, (3) Γ ⊧ φ iff there is ...

The Foundations: Logic and Proofs

... In English “or” has two distinct meanings. “Inclusive Or” - In the sentence “Students who have taken CS202 or Math120 may take this class,” we assume that students need to have taken one of the prerequisites, but may have taken both. This is the meaning of disjunction. For p ∨q to be true, either ...

... In English “or” has two distinct meanings. “Inclusive Or” - In the sentence “Students who have taken CS202 or Math120 may take this class,” we assume that students need to have taken one of the prerequisites, but may have taken both. This is the meaning of disjunction. For p ∨q to be true, either ...

Introduction to proposition

... “You can access the Internet from campus only if you are a computer science major or you are not a freshman.” Solution: There are many ways to translate this sentence into a logical expression. Although it is possible to represent the sentence by a single propositional variable, such as p, this woul ...

... “You can access the Internet from campus only if you are a computer science major or you are not a freshman.” Solution: There are many ways to translate this sentence into a logical expression. Although it is possible to represent the sentence by a single propositional variable, such as p, this woul ...

Discrete Structure

... Applications of Predicate Logic • It is the formal notation for writing perfectly clear, concise, and unambiguous mathematical definitions, axioms, and theorems (more on these in module 2) for any branch of mathematics. • Predicate logic with function symbols, the “=” operator, and a few proof-buil ...

... Applications of Predicate Logic • It is the formal notation for writing perfectly clear, concise, and unambiguous mathematical definitions, axioms, and theorems (more on these in module 2) for any branch of mathematics. • Predicate logic with function symbols, the “=” operator, and a few proof-buil ...

Section I(c)

... The statement x 5 2 is an example of a predicate. What does predicate mean? It is a statement with a unknown such as x . Once we substitute values for all the unknowns then it becomes a proposition. For example if we substitute x 3 then ...

... The statement x 5 2 is an example of a predicate. What does predicate mean? It is a statement with a unknown such as x . Once we substitute values for all the unknowns then it becomes a proposition. For example if we substitute x 3 then ...

notes

... Let P be a propositions containing the (distinct) atomic formulas A 1 , . . . , An and v1 , . . . v2n its interpretations. We denote with v P the boolean function associated with P , i.e. vP : {0, 1}n → {0, 1} is defined as follows: for each (a 1 , . . . , an ), ai ∈ {0, 1}, there exists i ∈ {1, . ...

... Let P be a propositions containing the (distinct) atomic formulas A 1 , . . . , An and v1 , . . . v2n its interpretations. We denote with v P the boolean function associated with P , i.e. vP : {0, 1}n → {0, 1} is defined as follows: for each (a 1 , . . . , an ), ai ∈ {0, 1}, there exists i ∈ {1, . ...

Solutions to Workbook Exercises Unit 16: Categorical Propositions

... U.D.: animals Bx: x barks Cx: x is a cat Lx: x likes to walk Dx: x is a dog Mx: x meows Fx: x likes canned food Wx: x wags its tail (a) Some dogs howl. ∃x (Dx • Hx) x ...

... U.D.: animals Bx: x barks Cx: x is a cat Lx: x likes to walk Dx: x is a dog Mx: x meows Fx: x likes canned food Wx: x wags its tail (a) Some dogs howl. ∃x (Dx • Hx) x ...

Document

... the truth, and knaves, who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” Example: What are the types of A and B? Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p re ...

... the truth, and knaves, who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” Example: What are the types of A and B? Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p re ...

Lecture 6 Induction

... • A proposition denoted by symbols P(n) are propositions having to do with all numbers of value n. • Terminology and notation: If we say that proposition P(n) is true for all natural numbers n, then we mean that: P(1) ∧ P(2) ∧ P(3) ∧ ... is true. That is the logical “and” of all of these proposition ...

... • A proposition denoted by symbols P(n) are propositions having to do with all numbers of value n. • Terminology and notation: If we say that proposition P(n) is true for all natural numbers n, then we mean that: P(1) ∧ P(2) ∧ P(3) ∧ ... is true. That is the logical “and” of all of these proposition ...

Propositional Logic

... Why study propositional logic? • A formal mathematical “language” for precise reasoning. • Start with propositions. • Add other constructs like negation, conjunction, disjunction, implication etc. • All of these are based on ideas we use daily to reason about things. ...

... Why study propositional logic? • A formal mathematical “language” for precise reasoning. • Start with propositions. • Add other constructs like negation, conjunction, disjunction, implication etc. • All of these are based on ideas we use daily to reason about things. ...

ch1_Logic_and_proofs

... 1. Assume p is true and q is false 2. Show that ~p is also true. 3. Then we have that p ^ (~p) is true. 4. But this is impossible, since the statement p ^ (~p) is always false. There is a contradiction! 5. So, q cannot be false and therefore it is true. ...

... 1. Assume p is true and q is false 2. Show that ~p is also true. 3. Then we have that p ^ (~p) is true. 4. But this is impossible, since the statement p ^ (~p) is always false. There is a contradiction! 5. So, q cannot be false and therefore it is true. ...

p q

... sentence that may be assigned a ‘true’ or ‘false’ value, but not both. This value is the truth value of the proposition. Propositions: “1+2=3”, “Peter is a programmer”, “It is snowing”. Not Propositions: “Is 1+2=3?”, “What a beautiful evening!”, “The number x is an integer”. Also Propositions: “Ther ...

... sentence that may be assigned a ‘true’ or ‘false’ value, but not both. This value is the truth value of the proposition. Propositions: “1+2=3”, “Peter is a programmer”, “It is snowing”. Not Propositions: “Is 1+2=3?”, “What a beautiful evening!”, “The number x is an integer”. Also Propositions: “Ther ...

Slide 1

... proof – Corollary: a theorem that can be directly established from a theorem that has been proved – Conjecture: a statement that is being proposed to be true ...

... proof – Corollary: a theorem that can be directly established from a theorem that has been proved – Conjecture: a statement that is being proposed to be true ...

Lecture01 - Mathematics

... Set Theory: Informally we define a set as a collection of objects. The resulting theory of how one can operate on sets is known as naïve set theory. It is naïve because the informal definition leads to subtle paradoxes. A more careful definition of set removes these paradoxes and leaves the conclusi ...

... Set Theory: Informally we define a set as a collection of objects. The resulting theory of how one can operate on sets is known as naïve set theory. It is naïve because the informal definition leads to subtle paradoxes. A more careful definition of set removes these paradoxes and leaves the conclusi ...

Braun Defended

... propositions (10) and (11) differ and hence differ in truth-value. This objection, however, ignores the distinction between the proposition expressed by a sentence, its assertoric content, and what contribution a sentence makes to complex sentences of which it is a part, its ingredient sense. If we ...

... propositions (10) and (11) differ and hence differ in truth-value. This objection, however, ignores the distinction between the proposition expressed by a sentence, its assertoric content, and what contribution a sentence makes to complex sentences of which it is a part, its ingredient sense. If we ...

Bernhard Placidus Johann Nepomuk Bolzano (Bernard Bolzano in English; 5 October 1781 – 18 December 1848) was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his antimilitarist views. Bolzano wrote in German, his mother tongue. For the most part, his work came to prominence posthumously.