Homework #16

Due Monday, November 14th

 

Page 479 and following – Exercises for section 7.1 

 

 #1     a  {( (0,0), (1,1), (2,2), (3,3)}

b  {(1,3), (2,2), (3,1), (4,0)}

          c  { (12,0), (2,0), (2,1), (3,0),(3,1), (3,1), (4,0), (4,1), (4,2), (4,3) }

 

#2     a        {( 1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2.4), (2.6), (3,3), (3,6), (4,4), (5,5), (6,6)}

b        Draw a line from a to b whenever a divides b

c        Put an x in the ith  row and jth column if and only if i divides j.

 

#3     a        Transitive

          b        Reflexive, symmetric, transitive

c        Symmetric

 

#24   R-1 = { (b,a) | (a, b) is an element of R} = ( (b,a) | a < b} = { (a,b) | a > b}

          R’  = { (a,b) | (a,b ) is not an element of R} = { ( a,b,) | a is not less than b} = { (a,b) | a >= b}

 

#28  a = { (1,1), (1,2), (2,1), (2,2) (2,3), (3,1), (3,2), (3,3), (3,4) } = R 2  

b = {  (1,2), (2,3), (3,4)} = R1      

c = { }

 

#30  Since (1,2) is an element of R  and (2,1) is an element of S,  we have (1,1) is an element of  S o R

          entire answer is  { (1,1), (1,2), (2,1), (2,2)}

 

 

Page  488 and following – Excercises for section 7.2

 

#1    { (1,2,3), (1,2,4), (1,3,4), (2,3,4)}

 

#2      (6,1,1,1), (1,6,1,1), (1,1,6,1), (1,1,1,6), (3,2,1,1), (3,1,2,1), (3,1,1,2), (2,3,1,1), (2,1,3,1), (2,1,1,3), (1,3,2,1), (1,3,1,2), (1,2,3,1), (1,2,1,3), (1,1,3,2), and (1,1,2,3)

 

#3     (Nadir, 122, 34, Detroit, 08:10), (Acme, 221, 22, Denver, 08:17), (Acme, 122, 33, Anchorage, 08:22), (Acme, 323, 34, Honolulu, 08:30), (Nadir, 199, 13, Detroit, 08:47), (Acme, 222, 22 Denver, 09:10), (Nadir, 322, 34, Detroit, 09:44) 

 

#10    The 5-tuples in  Table 7 that have A110 as their room are

          (Cruz, Zoology, 335, A100, 9:00 A.M.)

          (Cruz, Zoology, 512, A100, 8:00 A.M.)

          (Farber, Psychology, 601, A100, 3:00 P.M.)

 

#15   {P3.5.6}