Conditional Statements, Converse, and Counterexamples

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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. - PowerPoint PPT Presentation

Text of Conditional Statements, Converse, and Counterexamples

  • Warm Up:3x9x + 2946793xSolve for x in both figures.

  • Conditional StatementConditional statement has two parts, hypothesis and a conclusion.

    hypothesisconclusionIf ____________, then____________.

    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.

  • Rewrite in If-Then formTwo points are collinear if they lie on the same line. A seal swims.Two points are collinear- Lie on the same lineIf two points lie on the same line, then they are collinear.

    - Seal (animal)- Swims If the animal is a seal, then it swims.

  • Rewrite in If-Then formA number divisible by 9 is also divisible by 3.A square has four sides.

    Number divisible by 9- Divisible by 3If a number is divisible by 9, then it is also divisible by 3.

    Square- Four sidesIf it is a square, then it has four sides.

  • What is the Converse?If __________, then_________.

    hypothesisconclusionConditional StatementconclusionhypothesisIf the man eats donuts, then he must be a policeman.Converse StatementIf 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.

  • Converse or Conditional: which is true?State whether each sentence is true or false.TrueFalseIf you live in Los Angeles, then you live in California.

    If you live in California, then you live in Los Angeles.

    If today is Wednesday, then tomorrow is Thursday.If tomorrow is Thursday, then today is Wednesday.

    TrueTrueWrite the Converse? qp

  • CounterexampleAn example that proves a statement is FALSEIf you live in California, then you live in Los Angeles.

    Counterexample: Ms. McGregor lives in Huntington Beach, California.

  • Find a Counterexample for the following:If the animal has teeth, then it is a shark.

    If the shape has four right angles, then it is a square.

    TRUEFALSETRUEFALSE

  • Find a Counterexample for the following:All teachers are boring.

    Marys counterexample is her best friend Alexis that is a senior. They are never bored when they are together.

    Why isnt this a proper counterexample?

    Joes counterexample is Mrs. Lara. She gives tons of homework!

    Why doesnt this count as a counterexample?

  • Formal NotationConditional StatementIf (hypothesis), then (conclusion).p = hypothesis and q = conclusionIf p, then q.p implies qp q

  • Formal NotationConverse StatementIf (conclusion), then (hypothesis).If q, then p.q implies pq p

  • Find a CounterexampleIf 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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