MATH 140 Final Exam                                                            Name________________

Instructions: Answer all the questions on Part I and any five on Part II.  Show your work and clearly label your answers.

 

Part I (5 points apiece)

1.     How many numbers are there in the set {17, 25, 33, …801}?         1.____________

2.     If A={1,2,3,4} and B={3,4,5,6} find (AÈB)-(AÇB).                     2.____________

3.     If n(A)=12, n(B)=14, and n(AÈB)=16, find n(AÇB).                     3.____________

4.     Let A={x,y,z}, B={1,2,3,4}, and C={3,4,5,6}.  Find one  4.____________

       element of the set A´(C-B).

5.     If P is True and Q is False find the truth value of                  5.____________

      (PÙ~Q).

6.     Express 499 as a Roman numeral.                                       6.____________

7.     Express 399 as a base 5 numeral.                                                   7.____________

8.     Express 12T112 as a base ten numeral.                                            8.____________

9.     Find the GCD of 4200 and 2142.                                                   9.____________

10.  Find the LCM of 24, 189, and 375.                                               10.____________

11. A number increased by 12% equals 26.88. Find the number.           11.____________

12. Express as a fraction in lowest terms: .                    12.____________

13. Express  as a fraction in lowest terms.                                  13.____________

14. Give examples of two irrational numbers.                             14.____________

15.  Find d(840).                                                                                  15.____________

Part II - Answer any 5 of the 6 Questions. Each question is worth 15 points.

Question 1 - Sets

1.     Let the universal set U = {1,2,3,…,20).  Let A = {1,3,5,7,9}.  In each of the following find a set B that satisfies the given conditions. (If possible)

a)     n(B)=5 and n(A-B)=3.                                                    B=____________

b)     BÍA and n(A´B)=10.                                                    B=____________

c)     n(AÇB)=3 and n(A-B)=4.                                               B=____________

 

2.     Give an example of two sets that are equivalent but not equal.

 

 

 

 

 

 

 

 

 

 

Question 2  -  Number Theory

1.     Is 667 a prime?

 

 

 

2.     Find the prime factorization of 3528.

 

 

 

3.     Find the GCD of 1498 and 1778 using the Euclidean Algorithm.

 

Question 3 - Number Bases

1.     Express 1573 as a base twelve numeral.

 

 

 

2.     Which is the larger integer  -  4215 or 9412?

 

 

 

3.     Perform the operations in the given bases:

a)     2030105 -  131225 =                                                                    a)_____________

b)     312312 ¸T212 =                                                                            b)_____________

 

Question 4 - Arithmetic Operations

1.     Show that 2+7 = 9 using the set definition of addition.

 

 

 

 

2.     Show that 3x4 = 12 using the set definition of multiplication.

 

 

 

3.     Show why 2¸0 is undefined.

 

 

 

 

4.     Using the chip model demonstrate that (-7) - (-5) = -2.

 

Question 5 - Logic

1.     State the negation of the following sentence but do not begin your answer with the words “not” or “no”.     “All freshmen study very hard.”

 

 

2.     Determine if the following is a valid argument:

  Hypotheses  Q1:  

                       Q2:  

  Conclusion   C:     Q

 

 

 

 

3.     Determine if the following is a valid argument:

    Some even numbers are primes.

    No odd numbers are even.

    Therefore no odd numbers are primes.

 

 

 

 

Question 6  -  Venn Diagrams

1.     Shade the following set in the Venn Diagram: 

 

 

 

 

 

2.     Determine the number of elements in each part of the Venn diagram if n(U)=25, n(A)=12, n(B)=17, and n(AÈB)=24.

 

 

 

 

 

 

 3.  Determine the number of elements in each part of the Venn diagram if n(U)=20, n(A)=10, n(B)=11, n(C)=12, n(AÇB)=5, n(AÇC)=6, n(BÇC)=7, and n(AÇBÇC)=2.