The document contains examples and explanations of logical reasoning concepts including conditional statements, their converses, inverses, contrapositives, and biconditionals. It also includes examples of properties like reflexive, symmetric, and transitive properties. Venn diagrams and logic puzzles are presented. Worked examples show how to determine the order of steps to solve an equation and use clues to determine information.

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.

17. Need Help?

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