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Logical Statements and Conclusions in Mathematics

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Understand conditional, converse, inverse, and contrapositive statements with examples in symbolic and sentence form. Complete textbook assignments on page 91 and 124.

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Logical Statements and Conclusions in Mathematics

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  1. Week 7 Warm Up 09.26.11 1) find the slope between the two points: ( 2, -9 ) and ( -13 , 21 )

  2. p hypothesis q conclusion → Reads as “implies” ( then ). Ex 1 Conditional Statement: Ifthe sun is out, thenthe weather is good. q p If p then q. p →q

  3. Ex 2 Converse Statement: If the weather is good, then the sun is out. q p If q then p. q →p Ex 3 Biconditional Statement: p if and only if q. p ↔q

  4. Ex 4 p : The value of x is -5. q : The absolute value of x is 5. Write p→ qin words. If the value of x is -5, then the absolute value of x is 5. Write q→ pin words. If the absolute value of x is 5, then the value of x is -5.

  5. ∼ the symbol for negation Ex 5 Statement: ∠ 3 measures 90⁰. p ∠ 3 is not acute. q ∼p ∠ 3 does not measure 90⁰. Negation: ∠ 3 is acute. ∼q

  6. Ex 6 p: “the car will start.” q: “the battery is charged.” p →q Conditional Statement: If the car will start, then the battery is charged. q →p Converse: If the battery is charged, then the car will start. ∼p → ∼q Inverse: If the car will not start, then the battery is not charged. ∼q → ∼p Contrapositive: If the battery is not charged, then the car will not start.

  7. Review ∼ is the symbol for __________________. Do: 1 Write the conditional, converse, inverse and contrapositive in symbolic form and sentence form: p : ∠A is a right angle. q : The measure of ∠A is 90⁰. Assignment: Textbook Page 91, 8 – 20 All. Page 124, 2 – 12 evens.

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