Top Banner
Find your new seat
35

Find your new seat. Belonzi, Alison – (1,2) Benjamin, Jeremy – (1,3) Falkowski, Taylor – (1,4) Kapp, Timi – (2,1) Lebak, Allyson – (2,2)

Jan 04, 2016

Download

Documents

Lee Tyler
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Find your new seat

Page 2: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Belonzi, Alison – (1,2) Benjamin, Jeremy – (1,3) Falkowski, Taylor – (1,4) Kapp, Timi – (2,1) Lebak, Allyson – (2,2) Mikhailik, Alexis– (2,4)

Patterson, Ashley– (3,2)

Qureshi, Iman– (3,3) Rojas, Cheyenne–

(3,4) Schipske, George–

(4,2) Wood, Cara– (4,3)

Page 3: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Aufiero, Tyler – (1,1) Bester, Deaven – (1,2) Cantale, Anthony – (1,3) Carroll, McKenzie – (1,4) Chance, Erika – (2,1) Chung, Victoria – (2,2) Goodenough, Joseph –

(2,3) Jabs, Kelsey – (2,4) Knighten, Joshua – (3,1) Kokotajlo, Katelynn – (3,2) London, Chisara – (3,3)

Magowan, Jacob – (3,4) Nolan, Lydia – (4,1) Patterson, Ross – (4,2) Smylie, Heather – (5,1) Sprouse, Samuel – (5,2) Thompson, Caitlyn – (5,3) Valentine, Christopher –

(6,1) Whitbeck, Jesse – (6,2) Phillips, Brittany – (6,3)

Page 4: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Deductive reasoning is when you start from a statement you assume to be true, and draw conclusions that must be true if your assumptions are true.

For Example

All dogs have a tail.

Buddy is a dog.

Therefore Buddy has a tail.

Page 5: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

SYLLOGISM– A type of logic in which one goes from a general statement to a specific instance.

The classic exampleAll men are mortal. (major premise)Socrates is a man. (minor premise)Therefore, Socrates is mortal. (conclusion)

Page 6: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Inductive Reasoning, involves going from a series of specific cases to a general statement. The conclusion in an inductive argument is never guaranteed. (Based on observations)

Example: What is the next number in the sequence 6, 13, 20, 27,…

There is more than one correct answer.

Page 7: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Here’s the sequence again 6, 13, 20, 27,… Look at the difference of each term. 13 – 6 = 7, 20 – 13 = 7, 27 – 20 = 7 Thus the next term is 34, because 34 – 27 = 7. However what if the sequence represents the

dates. Then the next number could be 3 (31 days in a month).

The next number could be 4 (30 day month) Or it could be 5 (29 day month – Feb. Leap year) Or even 6 (28 day month – Feb.)

Page 8: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Deductive reasoning may not be the most accurate way of solving a problem, cause we all know that assumptions can be wrong.

Example:1. All Graduates of M.I.T. are Engineers

George is not from M.I.T.Therefore George is not an Engineer

2. Everybody from Texas is a cowboyScott is from TexasScott is a cowboy

Page 9: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Determine if the conjecture is true or false based on the given information. If it is false give a counterexample.

a) Given: angle A and angle B are supplementary. Conjecture: angle A and angle B are not congruent.

b) Given: line AB, line BC, line AC. Conjecture: A, B, and C are collinear.

c) Given: angle A and angle B are vertical angles.Conjecture: angle A and angle B are congruent.

Page 10: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Conditional or if then statements – an event will occur if another event happens◦ ______________ (p): the portion immediately

following ‘_____’◦ ______________ (q): the part immediately following

‘_____’◦ p→q

Page 11: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Identify the hypothesis and conclusion.1. If you miss practice, then you will not play

in the game.2. If you don’t study for the test, then you will

fail.Write in if-then form.1.An angle of 40° is acute.2.Collinear points lie on the same line.3.Congruent angles have the same measure.4.What goes up must come down.

Page 12: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

You can form another ________ statement by _______________ of a conditional.

This new statement is called the converse of the original conditional .

Page 13: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

1. If an animal is a fish, then it can swim.

2. Vertical angle are congruent.

3. An angle that measures 120° is obtuse.

Page 14: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Postulates are principles that are accepted to be __________.

Complete each postulate.1. Through any ________ points there is exactly one

_________.2. Through any ________ points not on the same lin3

there is exactly one _________.3. A _____ contains at least ______ points.4. A ________contains at least _______ points not on the

same __________.5. If _______ points lie in a plane, then the entire ______

containing those points lie in that __________.6. If two planes _________, then their intersection is a

_________.

Page 15: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Postulates1) R, S, and T are collinear. 2) There is only one plane that contains all the points R, S, and Q.

3) <PQT lies in plane N.

4) <SPR lies in plane N

5)If X and Y are two points on line Mm then line XY intersect plane N at P

6)Point K is on plane N

7)N contains RS

8) T lies in plane N

9) R, P, and T are coplanar.

10)Line L and line M intersect.

In the figure, P, Q, R and S are in Plane N. Use the postulates you have learned to determined whether each statement is true or false.

Page 16: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Syllogism: An argument composed of two statements or premises (the major and minor premises), followed by a conclusion.

For any given set of premises, if the conclusion is guaranteed, the arguments is said to be valid.

If the conclusion is not guaranteed (at least one instance in which the conclusion does not follow), the argument is said to be invalid.

BE CARFEUL, DO NOT CONFUSE TRUTH WITH VALIDITY!

Page 17: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Examples:1. All students eat pizza.

Claire is a student at ASU.Therefore, Claire eats pizza.

2. All athletes work out in the gym. Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym.

Page 18: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

3. All math teachers are over 7 feet tall. Mr. Severino is a math teacher. Therefore, Mr. Severino is over 7 feet tall. The argument is valid, but is certainly not true. The above examples are of the form If p, then q. (major premise) x is p. (minor premise) Therefore, x is q. (conclusion)

Page 19: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

______________: A diagram consisting of various overlapping figures contained in a rectangle called the universe.

A

B

This is an example of all A are B. (If A, then B)

Page 20: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

A B

This is an example of No A are B.

A B This is an example of some A are B.(At least one A is B)

Page 21: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Examples: Make a Venn Diagram to see if the argument is valid.

1. All smiling cats talk.The Cheshire Car SmilesTherefore, the Cheshire Cat talks.

2. No one who can afford health insurance is unemployed.All politicians can afford heath insurance.Therefore, no politician is unemployed.

3. Some professors wear glasses.Mr. Einstein wears glasses.Therefore, Mr. Einstein is a professor.

Page 22: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Things that talk

Smiling cats

x

Page 23: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

X=politician. The argument is valid.

People who can affordHealth Care.

Politicians

X

Unemployed

Page 24: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

#16 Some professors wear glasses. Mr. Einstein wears glasses.

Therefore, Mr. Einstein is a professor. Let the pink oval be professors, and the gray oval be glass

wearers. Then x (Mr. Einstein) is in the blue oval, but not in the overlapping region. The argument is invalid.

X

Page 25: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Law of Detachment: If p→q is true and p is true then q is true.

p p→q q

T T T

Page 26: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Example #1) ◦ Assume that “If a vehicle is a car, then it has four

wheels” is a true statement (p→q ). ◦ A sedan is a car (p). ◦ State a valid conclusion (q).

A sedan had four wheels.

Page 27: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Determine if statement (3) follows from (1) and (2)

(1) If Julie works after school, then she works in a department store.

(2) Julie works after school.(3) Julie works in a department store.

Page 28: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Determine whether a conclusion can be reached from the two statements.

(1) If Jim is a Texan, then he is an American.(2) Jim is a Texan.(3) ???

Page 29: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

(1) If October 12 is a Monday, then October 13 is a Tuesday.

(2) October 12 is a Monday.(3) ???

Page 30: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

(1) If Spot is a dog, then he has four legs.(2) Spot has four legs.(3) ???

Page 31: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

If and are true conditionals, then is also true.

Example: If someone lives in Mansfield, then they live in New Jersey. If someone lives in New Jersey, then they live in the United States. The conclusion then would be: “If someone lives in Mansfield, then they live in the United states.”

p q q rp r

Page 32: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Determine whether the conclusion is valid using the law of syllogisms.

(1) If William is reading, then he is reading a magazine.

(2) If William is reading a magazine, then he is reading a magazine about computers.

(3) If William is reading, then he is reading a magazine about computers.

Page 33: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

(1) If a metal is liquid at room temperature, then it is mercury.

(2) If a metal is mercury, then its chemical symbol is Hg.

(3) If a metal is liquid at room temperature, then its chemical symbol is Hg.

Page 34: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Make a conclusion.(1) If a number is a whole number, then it is

an integer.(2) If a number is an integer, then it is a

rational number. (3) Conclusion:

Page 35: Find your new seat.  Belonzi, Alison – (1,2)  Benjamin, Jeremy – (1,3)  Falkowski, Taylor – (1,4)  Kapp, Timi – (2,1)  Lebak, Allyson – (2,2)

Make a conclusion:(1) If people live in Manhattan, then they live

in New York.(2) If people live in New York, then they live in

the United States.(3) Conclusion: