WARM UP. DEDUCTIVE REASONING LEARNING OUTCOMES I will be able to use the law of detachment and syllogism to make conjectures from other statements I.

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Presentation transcript:

WARM UP

DEDUCTIVE REASONING

LEARNING OUTCOMES I will be able to use the law of detachment and syllogism to make conjectures from other statements I will be able to use inductive and deductive reasoning to make conjectures about given information

SYMBOLIC NOTATION p  q The  means implies. p represents the hypothesis of a conditional statement, and q represents the conclusion. p  q also means If p, then q.

SYMBOLIC NOTATION How could we use symbolic notation to write the converse of a statement? q  p What about the inverse of a statement? ~p  ~q What about the contrapositive of a statement? ~q  ~p

SYMBOLIC NOTATION Let p be “the value of x is -7” and let q be “the absolute value of x is 7.” Write p  q, q  p, then determine if the biconditional statement is true.

SAGE AND SCRIBE

TYPES OF REASONING Deductive reasoning is making a conjecture based on facts, definitions, and accepted properties in a logical order. Fact: In the picture, angle 1 and angle 2 are vertical angles. Conjecture: Since we know that vertical angles are congruent, we could make the conjecture that angle 1 and angle 2 are congruent

DEDUCTIVE OR INDUCTIVE? My daughter has gymnastics every Tuesday. Yesterday was Tuesday, therefore my daughter had gymnastics. For the past three Fridays the Lancers have played a football game. Dana concludes that the Lancers will play this Friday. If you live in Texas, you must take driver’s education, have a driver’s permit at age 15, and pass a driving test to get your license. Marcus lives in Texas. He is 16 years old and has his license. Therefore, Marcus took driver’s education and passed his driver’s test.

DEDUCTIVE REASONING PUZZLE Find a partner!

LAW OF DETACHMENT If p → q is a true conditional statement and p is true, then q is true. (1) If you save a penny, then you have earned a penny. (2) Art saves a penny. What is the logical conclusion? Art earned a penny

LAW OF SYLLOGISM If p → q and q → r are true conditional statements, then p → r is true. (1) If you are a teenager, then you are always right. (2) If you are always right, then people will listen to you. What is the statement that follows logically? (3) If you are a teenager, then people will listen to you.

LAW OF DETACHMENT VS. LAW OF SYLLOGISM

EXIT TICKETHOMEWORK Use the law of detachment or the law of syllogism to complete the statement. Pg. 91: 8-15, 21-25, 30-35