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PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

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Page 1: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+ 2.2: Analyze Conditional Statements

Page 2: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+Conditional Statement Has two parts…

*Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To be false, only one counterexample is needed

Page 3: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+

Page 4: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+

1. If an angle is 90 degrees, then it is a right angle

2. If x = -3, then 2x + 7 = 1

3. If n = 9, then n squared is 81

4. If tourists are at the Alamo, then they are in in TX

Page 5: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+Negation: Opposite of the original statement

Page 6: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+Related Conditionals

  Conditional Statement: Hypothesis and Conclusion

  Inverse: Negate Conditional Statement

  Converse: Exchange Hypothesis and Conclusion

  Contrapositive: negate the Converse

**Equivalent Statements

Page 7: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+

  Conditional Statement: Hypothesis and Conclusion

  Inverse: negate Conditional Statement

  Converse: Exchange Hypothesis and Conclusion

  Contrapositive: negate the Converse

If you are a guitar player, then you are a musician

If you are a musician, then you are a guitar player

If you are NOT a guitar player, then you are NOT a musician

If you are NOT a musician, then you are NOT a guitar player

Page 8: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+

  Conditional Statement: Hypothesis and Conclusion

  Inverse: negate Conditional Statement

  Converse: Exchange Hypothesis and Conclusion

  Contrapositive: negate the Converse

If a dog is a Great Dane, then it is large

If a dog is large, then it is a Great Dane

If a dog is NOT a Great Dane, then it is NOT a dog

If a dog is NOT large, it is NOT a Great Dane

On your own: Related Conditionals

Page 9: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+

  Conditional Statement: Hypothesis and Conclusion

  Inverse: negate Conditional Statement

  Converse: Exchange Hypothesis and Conclusion

  Contrapositive: negate the Converse

If a polygon is equilateral, then the polygon is regular

If a polygon is regular, then the polygon is equilateral

If a polygon is NOT equilateral, then it is NOT regular

If a polygon is NOT regular, then the polygon is NOT equilateral

On your own: Related Conditionals

Page 10: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+Definitions of words Can be written as conditional statements (if-then) and or as its converse. Both are true

Page 11: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+Biconditional Statement Any true definition can use the phrase “if and only if” in a statement because both the conditional statement and its converse are true.

Page 12: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+ Rewrite the statement as biconditional “If Mary is in theater class, she will be in the fall play. If Mary is in the fall play, she must be taking theater class”

Biconditional: “Mary is in the theater class IF AND ONLY IF she will be in the fall play.”

“Mary will be in the fall play IF AND ONLY IF she is in theater class.”

OR

Page 13: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+ Decide Whether Each Statement about the Diagram is True or False

TRUE!

FALSE!

TRUE!

Page 14: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+ Decide whether each statement is true or false

SO TRUE!

SO TRUE!

SO FALSE!

SO FALSE!

Page 15: PDF 2.2 Analyze Conditional Statements€¦ · Conditional Statement Has two parts… *Can be true or false. To be true, conclusion must be true EVERY time hypothesis is true. To

+Homework: p. 82 (1-29)


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