Chapter 2 Reasoning and Proof. AIM: Introduction to Logic What types of statements are considered mathematical ? Statements in which truth value (either.

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Presentation transcript:

Chapter 2 Reasoning and Proof

AIM: Introduction to Logic What types of statements are considered mathematical ? Statements in which truth value (either true of false) can be established are considered mathematical statement. In terms of “English,” interrogative statements, imperative statements, or fragments are NOT considered mathematical statements.

What are some example of mathematical and non- mathematical sentences? Math Sentences Congruent angles are angles that have the same measure. 17 – 5 = 12 The Brooklyn Bridge is in New York. The Brooklyn Bridge is in California. Non-Math Sentences Did you have soccer practice today? Go to your room. Every parallelogram 19 – 2

None of these sentences have variables. When does that come into play? These are called open sentences. The variables can be replaced by numbers. In the English language, pronouns are comparable to variables in math.

Specific Types of Mathematical Sentences Vocabulary wordMeaningSymbol Used When are these types of statements “true?” NegationThese have the opposite truth value of a given statement. ~ If the original is true, the negation is false. If the original is false, the negation is true. ConjunctionA compound sentence using the connective “and.” ^ Both parts of the statement need to be true in order for the statement to be true. DisjunctionA compound sentence using the connective “or.” V Only one part needs to be true to form a true statement. ConditionalA compound sentence using the connectives “If….then….” ***This requires more space, and another day.****

Let’s Practice!! State whether each of the following is a mathematical sentence. 1)Thanksgiving is on the fourth Thursday in November. 2)Where did you go? 3)Y – 7 = 3y + 4

Write the negation of each sentence. 1)The school has an auditorium. 2)Michigan is not a city. 3)A stop sign is painted red. 4)Today is not Wednesday

Let p represent: “It is hot.” Let q represent: “It is raining.” Let r represent: “The sky is cloudy.” Write each sentence in symbolic form: 1. It is hot and it is raining. 2. It is not hot. 3. It is raining and the sky is not cloudy. 4. It is hot and the sky is cloudy. 5. It is not hot and the sky is cloudy. 6. It is not hot and it is not raining.

Using the truth value for each given statement, tell if the conjunction is true or false. A piano is a percussion instrument.(TRUE) A piano has 88 keys(TRUE) A flute is a percussion instrument.(FALSE) A trumpet is a brass instrument.(TRUE) 1. A flute is a percussion instrument and a piano is a percussion instrument. 2. A piano has 88 keys and is a percussion instrument. 3. A flute is not a percussion instrument and a trumpet is a brass instrument.