CST 24 – Logic.

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Presentation transcript:

CST 24 – Logic

uses examples, or several observations to make conclusions INDUCTIVE REASONING uses examples, or several observations to make conclusions CONJECTURE A conclusion based on inductive reasoning.

uses facts, definitions, rules, properties to draw conclusions. DEDUCTIVE REASONING uses facts, definitions, rules, properties to draw conclusions.

Ex 1: Answer the following questions Ex 1: Answer the following questions. Then determine if it is inductive or deductive reasoning. a. Find the next number in the sequence: 2, 4, 8, ... 16 inductive

deductive b. Name the property for each statement. given distribute subtraction division deductive

c. The area of a square is 49 square units c. The area of a square is 49 square units. Find the perimeter of the square. 7 P = 28 A = 49 7 7 deductive 7

d. Marco gets up at 6am every day. What time will he get up next Monday? inductive

e. The definition of a composite number is being divisible by another number besides 1 and itself. Therefore, 12 is a composite number. deductive

If _________, then ________. CONDITIONAL STATEMENT If _________, then ________. HYPOTHESIS Statement following the “if” CONCLUSION Statement following the “then”

hypothesis conclusion hypothesis conclusion Ex 2: State the hypothesis and conclusion of the given conditional statement: a. If you give a mouse a cookie, then he will want some milk. hypothesis conclusion b. If a number is even, then it is divisible by 2. hypothesis conclusion

Assuming “If”, the “then” MUST happen TRUE STATEMENT Assuming “If”, the “then” MUST happen FALSE STATEMENT Assuming “If”, the “then” might or might not happen COUNTEREXAMPLE One example that proves statement false

Ex 2: Determine if the statement is true or false Ex 2: Determine if the statement is true or false. If false, provide a counterexample: a. If you drive a mustang, then it is red. False, black

Ex 2: Determine if the statement is true or false Ex 2: Determine if the statement is true or false. If false, provide a counterexample: b. If a number is prime, then it is only divisible by 1 and itself. True

Ex 2: Determine if the statement is true or false Ex 2: Determine if the statement is true or false. If false, provide a counterexample: c. If you take the opposite of a number, then it is less than the original number. False, -3