MAT104 Algebra with Applications Week 6 Set and Logic Homework 14 Questions

1.) Give the number of elements in the region Marked I,II,III,IV,V,VI,VII,VIII in the figure

2.) Human blood is typed Rh+ (positive blood) or Rh- (Negative blood). This Rh factor is called antigen . There are two other antigens known as A and B types. Blood lacking both A and B types is called type O. Sketch a venn diagram showing the 3 types of antigens , A and B and Rh and label each of the eight regions. For example O+ is inside the Rh set (anything in Rh is positive) but outside both A and B . On the other hand ,O- is that region outside all three circles.

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3.) From a survey of 100 college students, marketing research company found that 55 students owned iphones, 30 owned cars and 20 owned both iphones and cars:

How many students owned either car or iphone (but not both)?

How many students do not owned either a car or an iphone?

4.) In a recent survey of 100 women, the following information was gathered.

35 uses shampoo A.

30 uses shampoo B.

37 uses shampoo C.

8 uses shampoo A and B

6 uses shampoo A and C

10 uses shampoo B and C

3 uses all 3

Use the figure to answer the question in the problem.

How many are using shampoos A and C, but not B (Region IV)?

5.) In a recent survey of 100 women, the following information was gathered.

40 uses shampoo A

48 uses shampoo B

45 uses shampoo C

23 uses shampoos A and B

10 uses shampoos A and C

6 uses shampoos B and C

3 uses all three

Use the figure to answer the question in the problem

How many are using shampoo A only (Region I)?

6.) A poll was taken of 100 students at a computer campus to find out how they got to campus. The results are below. How many are not using any of the 3?

33 said they drove alone

34 rode in a carpool

34 rode public transportation

7 uses both carpool and public transportation

7 uses both carpool and sometimes their own cars

6 uses buses as well as their own cars

2 uses all three method

7.) A poll was taken of 100 students at a computer campus to find out how they got to campus. the results are below.

27 said they drove alone

43 rode in a carpool

32 rode public transportation

10 uses both carpool and public transportation

5 uses both carpool and sometimes their own cars

2 uses buses as well as their own cars

1 uses all three method

Use the figure to answer the question in the problem

How many are using all of the 3 (Region VII)?

8.)At the time of George W. Bush presidency, there have been 43 president of United States. Draw a Venn Diagram showing the following facts about where each served before assuming presidency. How many presidents served as Vice-presidents and in the senate, but did not served in a cabinet post?

14 were vice-pres

6 served in the senate

15 held a cabinet post

2 were VP and served in the senate

8 were VP and held a cabinet post

4 served in the senate and held a cabinet post

1 was VP, in the senate, and held a cabinet post

9.) Answer the question and tell whether it illustrates inductive or deductive reasoning.

A.) What is the 50th consecutive even number?

B.)Is it illustrates inductive or deductive reasoning?

10.) Do the following:

A.) What is the sum of the first 65 consecutive odd number?

B.) What is the sum of the first 650 consecutive odd number?

11.) Compute the following:

A.) 9 x 1 – 1 =

B.) 9 x 21 – 1 =

C.) 9 x 321 – 1 =

12.) Tell whether you believed that the conjecture in the problem is true or false?

The product of two primes is prime.

13.) Use venn diagrams to check the validity of the argument

All candy is fattening.

All candy is delicious.

Therefore, all fattening food is delicious

All snarks are fribbles

All fribbles are ugly

Therefore all snarks are ugly

No professors are ignorant

All ignorant people are vain

Therefore no professors are vain.

14.) Use Venn Diagrams to check the validity of the arguments in the problem below

All red hair is pretty. No pretty things are valuable. Therefore ALL red hair is valuable.