Relations

Read sections 7.1, 7.2, and 7.3

  1. Let S = {1,2,3}. Define a relation R on S which is reflexive. 
  2. Say we have a set which represents the months of the year. S = {January, February, March, April, May, June, July, August, September, October, November, December}. Define an equivalence relation R where for x in S, f(x) is the letter that the month starts with.  Give the equivalence classes (partitions) of S under R.  
  3. On page 304, a matrix is shown with columns ordered from 0 to 9, and then the columns (and corresponding rows) are rearranged to show a different ordering. Why? What does this new ordering represent? 
  4. Let S = {1,2,3,4,5} and R be a relation on S where R = { (1,1), (1,3), (1,5), (2,2), (2,4), (3,3), (3,5), (4,4), (5,5) } 

    Is R an order relation on S? Is R a partial ordering on S? Is R a total ordering on S? 

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