Geometry Honors Section 2.2 Introduction to Logic.

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Geometry Honors Section 2.2 Introduction to Logic

Complete the Venn diagram to represent the statement “All whales are mammals”. whales mammals

Venn diagrams are also called ______ diagrams, after the Swiss mathematician ____________. Euler Leonard Euler

You should be able to see from the diagram that the following statement is true. (1) If an animal is a whale, then it is a mammal.

If-then statements like statement (1) are called *___________ In a conditional statement, the phrase following the word “if” is the *_________. The phrase following the word “then” is the *_________. conditionals. hypothesis conclusion

If you interchange the hypothesis and the conclusion of a conditional, you get the *converse of the original conditional.

Example: Write a conditional with the hypothesis “an animal is a reptile” and the conclusion “the animal is a snake”. True or false? What is a counterexample? If an animal is a reptile than it is a snake. False

Write the converse of the conditional. True or false? If an animal is a snake, then it is a reptile. True

Consider the following statements: If a car is a corvette, then it is a Chevrolet. Susan’s car is a corvette. Complete the Euler diagram including an * to represent Susan’s car. Does this mean that Susan’s car is a Chevrolet? corvette chevrolet yes

Conditionals can be linked together to form logic chains. (It does not matter whether the conditionals are true.)

Example: Consider the following conditionals. If cats freak, then mice frisk. If sirens shriek, then dogs howl. If dogs howl, then cats freak. Prove the conditional “If sirens shriek, then mice frisk.” follows from the 3 given conditionals by arranging the 3 conditionals in the proper order. If sirens shriek, then dogs howl. If dogs howl, then cats freak. If cats freak, then mice frisk