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Conditional Statements, Converse, and Counterexamples

Conditional Statements, Converse, and Counterexamples. Warm Up:. 93°. 94°. 3x. 9x + 2. 67°. x. Solve for x in both figures. Conditional Statement. Conditional statement has two parts, hypothesis and a conclusion. If the man eats donuts, then he must be a policeman.

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Conditional Statements, Converse, and Counterexamples

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  1. Conditional Statements, Converse, and Counterexamples

  2. Warm Up: 93° 94° 3x 9x + 2 67° x Solve for x in both figures.

  3. Conditional Statement • Conditional statement has two parts, hypothesis and a conclusion. If the man eats donuts, then he must be a policeman. If the animal has four legs, then it must be a dog. If the bug stings, then it must be a wasp. If ____________, then____________. hypothesis conclusion

  4. Two points are collinear if they lie on the same line. A seal swims. - Seal (animal) - Swims • Two points are collinear • - Lie on the same line • If two points lie on the same line, then they are collinear. If the animal is a seal, then it swims. Rewrite in If-Then form

  5. A square has four sides. A number divisible by 9 is also divisible by 3. • Square • - Four sides • Number divisible by 9 • - Divisible by 3 If a number is divisible by 9, then it is also divisible by 3. • If it is a square, then it has four sides. Rewrite in If-Then form

  6. What is the Converse? If the man eats donuts, then he must be a policeman. If __________, then_________. If he is a policeman, then he must eats donuts. If the animal has four legs, then it must be a dog. If it is a dog, then it must have four legs. Conditional Statement Converse Statement hypothesis hypothesis conclusion conclusion

  7. Write the Converse? qp Converse or Conditional: which is true? • State whether each sentence is true or false. False • If you live in California, then you live in Los Angeles. • If you live in Los Angeles, then you live in California. True • If today is Wednesday, then tomorrow is Thursday. True • If tomorrow is Thursday, then today is Wednesday. True

  8. Counterexample • Anexamplethat proves a statement is FALSE • If you live in California, then you live in Los Angeles. • Counterexample:Ms. McGregor lives in Huntington Beach, California.

  9. Find a Counterexample for the following: TRUE FALSE If the animal has teeth, then it is a shark. TRUE If the shape has four right angles, then it is a square. FALSE

  10. Find a Counterexample for the following: All teachers are boring. Mary’s counterexample is her best friend Alexis that is a senior. They are never bored when they are together. Why isn’t this a proper counterexample? Joe’s counterexample is Mrs. Lara. She gives tons of homework! Why doesn’t this count as a counterexample?

  11. Formal Notation • Conditional Statement • If (hypothesis), then (conclusion). • p = hypothesis and q = conclusion • If p, then q. • p implies q • p q

  12. Formal Notation • Converse Statement • If (conclusion), then (hypothesis). • If q, then p. • q implies p • q p

  13. Find a Counterexample • If a something has four wheels, then it is used for transportation. • If an animal has spots, then it is a leopard. • Two lines in a plane always intersect in exactly one point. • If two lines are parallel, then they do not intersect.

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