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A conditional is a statement that can be written in the If – Then form. If the team wins the semi-final, then it will play in the championship.

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If the team wins the semi-final, then it will play in the championship. The “If” part is called the Hypothesis. The “Then” part is called the Conclusion.

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Then p q Hypothesis Conclusion If If Then

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p q If Hypothesis Then Conclusion Conditional If Then Conclusion Converse Hypothesis q p ConclusionHypothesis

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If the team wins the semi-final, then it will play in the championship. Conditional Converse q p p q If it will play in the championship, then the team wins the semi-final. If the team plays in the championship, then it won the semi-final.

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If the team wins the semi-final, then they will play in the championship. Conditional Converse q p p q If the team plays in the championship, then they won the semi-final. Inverse ~ p ~ q If the team does not win the semi-final, then they will not play in the championship. Contrapositive ~ q ~ p If the team does not play in the championship, then they did not win the semi-final.

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All tigers are cats. Conditional Converse q p p q If an animal is a cat, then it is a tiger. Inverse ~ p ~ q If an animal is not a tiger, then it is not a cat. Contrapositive ~ q ~ p If an animal is not a cat, then it is not a tiger. If an animal is a tiger, then it is a cat.

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If an angle is acute, then it has a measure less than 90. Conditional Converse q p p q If an angle has a measure less than 90, then it is an acute angle. Biconditional p q If both the conditional and its Converse are true, then it can Be written as a biconditional. An angle is acute if and only if It has a measure less than 90. “if and only if”

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cgi-bin/msgQuiz.php4?isbn= &chapter=1&lesson=4

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Inductive or Deductive Reasoning? The Tigers scored over 80 in ten straight basketball games. The tigers will score 80 points in tonight's game.

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Inductive or Deductive Reasoning? If it is raining, the swim meet will be canceled. It is raining. Therefore, the swim meet will be canceled.

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Inductive or Deductive Reasoning? If Keri is late for her 11pm curfew, she will be on restriction for 2 weeks. Keri came home at 11:05pm. Keri is on restriction for 2 weeks. .

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Inductive or Deductive Reasoning? The cafeteria has served chicken salad every Wednesday for the past two months. It will serve chicken salad this Wednesday.

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Inductive or Deductive Reasoning? If 500 students attend a football game, the high school can expect concession sales to reach $300.

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Inductive or Deductive Reasoning? Concession sales were highest at the game attended by 550 students.

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(1) p q (2) p (3) q Notice how the original Conditional has been Broken apart into two pieces. (Detached)

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p q p q If you pass the driving test, then you will get your license. Brian passed his driving test. Brian got his license.

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(1) p q (2) q r (3) p r Notice how all three statements are conditionals with three basic ideas. The repeating part cancels out to give the conclusion.

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If you get your license, then you can drive to school. p q q r p r If you pass the driving test, then you will get your license. If you pass the driving test, then you can drive to school.

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Identify the p and q Is 2 nd statement a another conditional ? If yes, check for syllogism. If no, is it a p? Then check for Detachment. If it is not a conditional and not a p statement, Then there is NO CONCLUSION!

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1- If a student is enrolled at Lyons High, then the student has an ID number. 2- Joe Nathan is enrolled at Lyons High. 3- Joe Nathan has an ID number. p: student High q: student has an ID number Law of Detachment p q p q

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1- If your car needs more power, use Powerpack Motor Oil. 2- Marcus uses Powerpack Motor Oil. NO CONCLUSION p: car needs more power q: use Powerpack Motor Oil p q q

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1- If fossil fuels are burned, then acid rain is produced. 2- If acid rain falls, wildlife suffers. 3- If fossil fuels are burned, then wildlife suffers. p: fossil fuels are burned q: acid rain is produced. Law of Syllogism p q q r p r

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1- If a rectangle has four congruent sides, then it is a square. 2- A square has diagonals that are perpendicular. 3- A rectangle has diagonals that are perpendicular. p: a rectangle has four congruent sides q: it is a square INVALID p q q r 3- If a rectangle has four congruent sides, then its diagonals are perpendicular.

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Postulates Through any two points there exists exactly one line. If two points exist, then exactly one line passes through them.

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Postulates A line contains at least two points. If a line exists, then it contains at least two points.

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Postulates If two lines intersect, then their intersection is exactly one point.

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Postulates Through any three noncollinear points there exists exactly one plane. If three noncollinear points exist, then exactly one plane contains them.

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Postulates A plane contains at least three noncollinear points. If a plane exists, then it contains at least three noncollinear points.

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Postulates If two points lie in a plane, then the line containing them lies in the plane.

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Postulates If two planes intersect, then their intersection is a line.

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