TODAY’S OBJECTIVE: Standard: MM1G2

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TODAY’S OBJECTIVE: Standard: MM1G2 Geometry - Lesson 2.2 TODAY’S OBJECTIVE: Standard: MM1G2 Students will understand and use the language of mathematical argument and justification. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

Essential Question What is logic?

Conditionals (If-then form) Conditionals are if-then statements Ex: If you are fourteen, then you are a teenager. Ex: If x=10, then 2x=20.

Converse, Inverse, & Contrapositive Statement: if p then q Converse: if q then p Inverse: if not p then not q Contrapositive: if not q then not p Statement: If you do your math homework, then you get a good grade. Converse: If you get a good grade, then you do your math homework. Inverse: If you don’t do your math homework, then you don’t get a good grade. Contrapositive: If you don’t get a good grade, then you don’t do your math homework.

Negation Now, you try. Negate the following statement: The negation of statement p is "not p." The negation of p is symbolized by "~p." Now, you try. Negate the following statement: If you can eat something, then it is considered food. Negation: If you cannot eat something, then it is not considered food.

Biconditional A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow . The biconditional p q represents: "p if and only if q," where p is a hypothesis and q is a conclusion.

Inductive & Deductive Reasoning Also known as logical reasoning Systems for reaching logical conclusions Inductive reasoning: the process of arriving at a conclusion based on a set of observations. In itself, it is not a valid method of proof. Deductive reasoning: the process of arriving at a conclusion based on previously known facts. It is the way proofs are written.

Law of Syllogism The Law of Syllogism: If p → q is true, and q → r is true, then p r is also true. Use the Law of Syllogism to come to a conclusion in the following example.

Example: Given 1: If I study and work hard, then I get good grades. Given 2: If I get good grades, then I get into a good college. Therefore: If I study and work hard... ... I get into a good college!

Practice Time! In the textbook, write answers only! Do page 207 Set A Odd Numbers. Do page 209 Set B Even Numbers. Work in your groups Raise your hand, for help!