UNIT 2: REASONING AND

PROOF

True or False? Why?1. If you are in

Guangdong, you are in China.

2. If you are in China, then you are in Guangdong.

3. If you are in Shekou, then you are in Guangdong.

4. If you are in Guangdong, then you are in Shekou.

True or False? Why?

1. If an animal is a beagle, then it is a dog.

2. If animal is a dog, then it is a beagle.

3. All animals are dogs.

4. All dogs are animals.

5. Draw a Venn diagram that shows that all robins are birds, but not all birds are robins.

Animals

Dogs

Beagles

Logic & Reasoning Foldable

Half

Half

Logic & Reasoning Foldable

42 mm

Logic & Reasoning Foldable

ConditionalStatement

Converse

Inverse

Contrapositive

Biconditional

Title/Name

Logic & Reasoning Foldable

ConditionalStatement (2.1)

Converse (2.1)

Inverse (2.1)

Contrapositive(2.1)

Biconditional(2.2)

Title/Name Definition Example True or False?Counterexample

Symbolic Form

Conditional:

Made up of hyp. & concl.

Uses if..., then … Or …only if…

Two points are collinear only if they are on the same line.

OR

If two points are collinear, then they are on the same line.

http://www.cartoonstock.com/directory/c/conditional_offer.asp

Converse:

Switch hyp. & concl.

If two points are on the same line, then they are collinear.

http://www.free-extras.com/search/1/converse+batman+begins.htm

Inverse:

Negate both hyp. & concl. of cond.

If two points are not collinear, then they are not on the same line.

http://www.maniacworld.com/inverse-mohawk.html

Contrapositive:

Negate both hyp. & concl. Of converse

If two points are not on the same line, then they are not collinear.

Biconditional:

Conditional + converse Both must be true!

If two points are collinear, then they are on the same line.

If two points are on the same line, then they are collinear.

= Two points are collinear if and only if they are on the same line.

Create your own

At your table:Write a conditional statement based on a

school rule.Create the converse, inverse, contrapositive

and biconditional statements using the cutouts.

Determine if statements are true or false.○ If false, provide a counterexample.

What’s the converse?

1. If M is the midpoint of AB, then AM=AB. If AM=AB, then M is the midpoint of AB.

Logic & Reasoning Foldable

ConditionalStatement (2.1)

Converse (2.1)

Inverse (2.1)

Contrapositive(2.1)

Biconditional(2.2)

Title/NameSymbolic Form& How to read it

Law ofDetachment

Law ofSyllogism

Example

DefinitionDefinition

Example

Five sisters all have their birthday in a different month and each on a different day of the week. Using the clues below, determine the month and day of the week each sister's birthday falls.

1. Paula was born in March but not on Saturday. Abigail's birthday was not on Friday or Wednesday.

2. The girl whose birthday is on Monday was born earlier in the year than Brenda and Mary.

3. Tara wasn't born in February and her birthday was on the weekend.

4. Mary was not born in December nor was her birthday on a weekday. The girl whose birthday was in June was born on Sunday.

5. Tara was born before Brenda, whose birthday wasn't on Friday. Mary wasn't born in July.

Need Help?

Put the steps in order. Describe why.

1. 10y + 5 - 5 = 25 - 5

2. y = 2

3. 10y = 20

4. 10y = 20

10 10

5. 10y + 5 = 25http://www.electrical-picture.com/inductive-vs-deductive-reasoning/

Properties

Property Definition

Addition Property If a=b, then a+c=b+c

Subtraction Property If a=b, then a-b=b-c

Multiplication Property If a=b, then ac=bc

Division Property If a=b and c=0, then a/c=b/c

Distributive Property a(b+c)=ab+ac

Reflexive Propertya=a

Properties

http://www.earblessings.com/2010/06/twin-shadow-castles-in-snow.html

http://www.photoshopessentials.com/photo-effects/water-reflection/

Properties

Symmetric PropertyIf a=b, then b=a

http://www.cristinacabal.com/?p=373

Properties

Transitive PropertyIf a=b and b=c, then a=c

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