Math 105 Quiz 1 Answer Key

MATH 105 Fri 8:00, Room L-207

______ANSWER KEY__________________

QUIZ 1 September 11, 2008 1. (4 points) Circle “Inductive” or “Deductive” for the type of reasoning in each situation below: a. Sherlock Holmes says, “I recognize the smell of the smoke from your pipe as tobacco grown in Jamaica in the spring and sold at 157 Eston Lane.”

a.

Inductive Deductive Holmes derived his conclusion from his experience smelling tobacco smoke.

b. Inductive Deductive b. “If I shoot you, the one of two things will The speaker logically analyzes the happen: Either you die, or you don’t. If you die, no situation. problem. If you don’t die, either you are injured, or you don’t.” c. “You probably have the flu. There’s been a lot of that going around these past few days.”

c.

Inductive Deductive The person derives the conclusion that “you have the flu” from his/her observations of other patients.

d. No way Bob can beat Mary at chess.

d.

Inductive Deductive The person derives his/her conclusion from his/her observations of the way Bob and Mary play chess.

2. (3 points) 5% of what is 100?

A = P ⋅ B . Here, A = 100 and P = 5% = 0.05 B=

A 100 = = 2000 . Answer: 5% of 2000 is 100. P 0.05

3. Given: A = {1, 5, 7, 9} and B = {3, 4, 5, 6, 7} a. (1 point) Write down the roster form of A ∩ B ? The intersection A ∩ B consists of those elements that are both in A and also in B.

A ∩ B = {5, 7} b. (1 point) Write down the roster form of A ∪ B ? The union A ∪ B lumps together all elements in A and all elements in B.

A ∪ B = {1, 3, 4, 5, 6, 7, 9} c. (1 point) Calculate: n( A)+ n( B) − n( A ∩ B) . Is it equal to n( A ∪ B) ?

n(A) = 4; n(B) = 5; n( A ∩ B ) = 2. So, n( A)+ n( B) − n( A ∩ B) = 4 + 5 – 2 = 7. Yes, it is equal to n( A ∪ B )