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Proofs
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.                    Animals
2.   If animal is a
     dog, then it is a
     beagle.
                              Dogs
3.   All animals are dogs.
4.   All dogs are animals.
                             Beagles
5.   Draw a Venn diagram
     that shows that all
     robins are birds, but
     not all birds are
     robins.
Logic & Reasoning Foldable

      Half




   Half
Logic & Reasoning Foldable

                       42 mm
Logic & Reasoning Foldable
           Title/Name
           Conditional
           Statement

            Converse



            Inverse



          Contrapositive



           Biconditional
Logic & Reasoning Foldable
 Title/Name       Definition   Example   True or False? Symbolic Form
Conditional                              Counterexample
Statement (2.1)

  Converse
    (2.1)


  Inverse
    (2.1)

Contrapositive
    (2.1)

Biconditional
    (2.2)
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                 http://www.cartoonstock.com/directory/c/conditional_offer.asp

    collinear, then they are on
    the same line.
Converse:


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




If two points are on the same line, then
    they are collinear.
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
 Symbolic Form        Law of        Law of      Title/Name
 & How to read it   Detachment     Syllogism    Conditional
                                                Statement (2.1)

                      Definition   Definition      Converse
                                                     (2.1)


                                                    Inverse
                      Example      Example            (2.1)


                                                Contrapositive
                                                    (2.1)

                                                 Biconditional
                                                     (2.2)
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?
Proofs
Put the steps in order. Describe
   why.
  1.   10y + 5 - 5 = 25 - 5

  2.   y=2

  3.   10y = 20

  4.   10y = 20
       10 10
                              http://www.electrical-picture.com/inductive-vs-deductive-reasoning/

  5. 10y + 5 = 25
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
Properties
        Reflexive Property
          a=a




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



http://www.photoshopessentials.com/photo-effects/water-reflection/
Properties
   Symmetric Property
     If a=b, then b=a




                  http://www.cristinacabal.com/?p=373
Properties
   Transitive Property
     If a=b and b=c, then a=c




                   http://www.buzzfeed.com/iloverobots

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Proofs

  • 2. 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.
  • 3. True or False? Why? 1. If an animal is a beagle, then it is a dog. Animals 2. If animal is a dog, then it is a beagle. Dogs 3. All animals are dogs. 4. All dogs are animals. Beagles 5. Draw a Venn diagram that shows that all robins are birds, but not all birds are robins.
  • 4. Logic & Reasoning Foldable Half Half
  • 5. Logic & Reasoning Foldable 42 mm
  • 6. Logic & Reasoning Foldable Title/Name Conditional Statement Converse Inverse Contrapositive Biconditional
  • 7. Logic & Reasoning Foldable Title/Name Definition Example True or False? Symbolic Form Conditional Counterexample Statement (2.1) Converse (2.1) Inverse (2.1) Contrapositive (2.1) Biconditional (2.2)
  • 8. 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 http://www.cartoonstock.com/directory/c/conditional_offer.asp collinear, then they are on the same line.
  • 9. Converse: Switch hyp. & concl. http://www.free-extras.com/search/1/converse+batman+begins.htm If two points are on the same line, then they are collinear.
  • 10. 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
  • 11. Contrapositive:  Negate both hyp. & concl. Of converse  If two points are not on the same line, then they are not collinear.
  • 12. 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.
  • 13. 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.
  • 14. 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.
  • 15. Logic & Reasoning Foldable Symbolic Form Law of Law of Title/Name & How to read it Detachment Syllogism Conditional Statement (2.1) Definition Definition Converse (2.1) Inverse Example Example (2.1) Contrapositive (2.1) Biconditional (2.2)
  • 16. 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.
  • 19. Put the steps in order. Describe why. 1. 10y + 5 - 5 = 25 - 5 2. y=2 3. 10y = 20 4. 10y = 20 10 10 http://www.electrical-picture.com/inductive-vs-deductive-reasoning/ 5. 10y + 5 = 25
  • 20. 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
  • 21. Properties  Reflexive Property  a=a http://www.earblessings.com/2010/06/twin-shadow-castles-in-snow.html http://www.photoshopessentials.com/photo-effects/water-reflection/
  • 22. Properties  Symmetric Property  If a=b, then b=a http://www.cristinacabal.com/?p=373
  • 23. Properties  Transitive Property  If a=b and b=c, then a=c http://www.buzzfeed.com/iloverobots

Editor's Notes

  1. 2.1 warm up
  2. 2.1 opener cont.
  3. 2.2 opener
  4. 2.3 opener
  5. 2.3
  6. 2.4 opener