Mathematics in computing

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Reference no: EM13583

1. m mod n will have values ranging from  0 to n-1.     

    T or F

2. -39 MOD 5 and -38 MOD 6 are congruent.

     T or F

3. The base system of the value 467 must be either decimal or octal. 

     T or F     

4. The value 367 is a prime number.     

     T or F     

5. The value 527 has a maximum of 22 possible prime factors because the square root of 527 is 22+.

     T or F

6. A Permutation of the elements of a set is an ordered arrangement of the elements of the set.     

   T or F     

7. P(7,3) = 210

   T or F     

8. C(8,5) = 56    

   T or F     

9. Consider the following relations on {1, 2, 3 } :      

          R1 = { (1,1),  (2,2),  (3,3) },  and     

          R2 = { (1,2),  (1,3),  (2,3) }.     

          R1 is symmetrical and R2 is transitive     

    T or F     

10. Using members of the set {1, 3, 4, 5, 7, 8}, the next larger P(6,3) permutation after 453  is  454.     

     T or F

11. The Sum Rule is applied when the tasks to be performed are disjoint.     

     T or F     

12. According to the Pigeonhole principle, when (m+4) items are to be placed in (m+9) boxes, there will be more than one item in at least one box.     

     T or F

13. Pascal's Triangle yields the value of the coefficients of an algebraic expansion.     

     T or F

14. The probability of picking a "face" card (Jack, Queen or King) from a standard deck of playing cards is C(52,12).     

     T or F     

15. P(n,r) is equal to or greater than C(n,r) when n => 1.     

     T or F     

16. There are 139 positive integers not exceeding 634 that are divisible by either 7 or 11.     

     T or F     

17. The relation  An = an-1+ bn-2+ n + 2  is a linear, homogeneous relation of degree 2.

     T or F     

18. A brand of shirt comes in four basic colors, has male, female and unisex versions and has six sizes for each.  This brand has a maximum of 13 different varieties.

    T or F

PART B     

1. Determine:     

          A).   -53 MOD 7     

          B).   -74 MOD 8 

2. Determine the Base10 expansion of (D4B) Base16

3. Define if the each set of integers are mutually relatively prime.  Defend your conclusion.     

          A).   {8, 44, 55}     

          B).   {7, 15, 26, 29, 37, 42}

4. Find the prime factors of the value 29,058.  Show the result in proper exponential form.

5.  Given:     

          A =   85

          B =   553   

          Define by factoring:     

          A).   gcd (A, B)   show in exponential form     

          B).   lcm (A, B)   show in exponential form     

6. Using the Euclidean Algorithm, determine:       

          GCD (3960, 3900).     

7. Convert  (1011 1001) Base2  to:     

          A).   (          ) Base16     


          B).   (          ) Base10

8. Given 2614BASE10.  Determine the equivalent value in BASE3.

    Hint: Use the Euclidean Algorithm

9. Define: (show intermediate work)     

     A.  P(11,8) =     

     B.  C(12,6) =      

10. What is the coefficient of  ( x^3 y^5 )  in the expansion (2x - 4y)^8 ?  You may leave the answer in a proper intermediate form.

11. Each locker in a building is labeled with four upper-case alpha characters followed by three Base 16 characters.  What is the maximum number of different locker numbers that can be generated? 

12. A group of six fair coins are flipped eight times.  What is the probability that each result has three heads in each flip?

13. f(n)= 3*f(n/2) - 6 when n is even and f(1) = -2.

      a.  What is the value of f(4)?

      b.  What is the value of f(8)?

14. How many positive integers not exceeding 6573 are divisible by neither 6 nor 15?

15. Given |A| = |B| = |C| = 60,  |A INT B| = 25,

    |B INT C| = 35,  |A INT B INT C| = 15, and     

    |A  UNION  B  UNION  C| = 115 elements.

    |A INT C| = ?

16. List the next SIX terms of the lexicographic ordering of the n-tuple 27436 where each digit is in the set {2,3,4,6,7}.

17. Which lottery presents the player with the best odds for winning,  (A or B)?  Defend your answer.     

     A =  C(41,6)     

     B =  C(42,5)     

18. Determine if the following zero-one matrix is:

    a. reflexive          T or F           |  0  1  1  |     

    b. symmetric       T or F           |  1  1  0  |     

    c. transitive        T or F           |  1  0  1  |     


A. Develop the Basis Step of the algorithm to determine the number of terms (cardinality) of the union of n mutually intersecting sets.  Show your work.

    For example, the cardinality of the union of three mutually intersecting sets is C(3,1) + C(3,2) + C(3,3) = 3+3+1 = 7. 

B.  Determine the Base8 value of 1642Base9.

Reference no: EM13583


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