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.

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.

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.

Then

p q

Hypothesis Conclusion

If

If Then

p q

If Hypothesis Then Conclusion

Conditional

If Then Conclusion

Converse

Hypothesis

q p

Conclusion Hypothesis

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.

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.

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.

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 canBe written as a biconditional.

An angle is acute if and only ifIt has a measure less than 90.

“if and only if”

http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834817-6&chapter=1&lesson=4

Inductive or Deductive Inductive or Deductive Reasoning?Reasoning?

The Tigers scored over 80 in ten straight The Tigers scored over 80 in ten straight basketball games. The tigers will score 80 basketball games. The tigers will score 80 points in tonight's game.points in tonight's game.

Inductive or Deductive Inductive or Deductive Reasoning?Reasoning?

If it is raining, the swim meet will be If it is raining, the swim meet will be canceled. It is raining. Therefore, the swim canceled. It is raining. Therefore, the swim meet will be canceled.meet will be canceled.

Inductive or Deductive Inductive or Deductive Reasoning?Reasoning?

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

..

Inductive or Deductive Inductive or Deductive Reasoning?Reasoning?

The cafeteria has served chicken salad The cafeteria has served chicken salad every Wednesday for the past two months. every Wednesday for the past two months. It will serve chicken salad this Wednesday.It will serve chicken salad this Wednesday.

Inductive or Deductive Inductive or Deductive Reasoning?Reasoning?

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

Inductive or Deductive Inductive or Deductive Reasoning?Reasoning?

Concession sales were highest at the Concession sales were highest at the game attended by 550 students.game attended by 550 students.

(1) p q

(2) p

(3) q

Notice how the original

Conditional has been

Broken apart into two pieces.

(Detached)

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.

(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.

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.

Identify the p and q

Is 2nd 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!

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 enrolled @Lyons Highq: student has an ID number

Law of Detachment

p q

p

q

1- If your car needs more power, use Powerpack Motor Oil.

2- Marcus uses Powerpack Motor Oil.

NO CONCLUSION

p: car needs more powerq: use Powerpack Motor Oil

p q

q

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 burnedq: acid rain is

produced.

Law of Syllogism

p q

q r

p r

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 sidesq: it is a square

INVALID

p q

q r

3- If a rectangle has four congruent sides,

then its diagonals are perpendicular.

PostulatesPostulates

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

PostulatesPostulates

A line contains at least two points. A line contains at least two points.

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

PostulatesPostulates

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

PostulatesPostulates

Through any three noncollinear points Through any three noncollinear points there exists exactly one plane.there exists exactly one plane.

If three noncollinear points exist, then exactly one plane contains them.

PostulatesPostulates

A plane contains at least three noncollinear points.

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

PostulatesPostulates

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

PostulatesPostulates

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