April 30th, 2017, 06:39 PM  #1 
Newbie Joined: Apr 2017 From: dammam Posts: 2 Thanks: 0  solve these problems
Q6 Let R be the relation on the set A = {1, 2, 3, 4} defined by aRb if and only if 2a > b + 1. a) List the ordered pairs in R. b) Find the matrix representing R Q−7: [5 marks] Suppose that the relation R is defined on the set Z where aRb means a = ±b. Establish whether R is an equivalence relation giving your justifications 
May 1st, 2017, 09:14 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807  Quote:
Some ordered pairs will have "1". For what "b" is 1Rb? From the definition of R, that will be "b" such that 2(1)= 2 > b+ 1 so 1Rb will be an ordered pair if 2> b+ 1 or b> 1. That is, we have 1R2, 1R3, and 1R4. Do the same for a= 2, 3, and 4. Quote:
Quote:
1) For all a in Z, aRa (reflexive law). 2) If aRb then bRa (symmetric law). 3) if aRb and bRc then aRc (transitive law). I presume that the "±" means that "aRb" if and only if either a= b or a= b. 3) (transitive law) if aRb then either a= b or a= b. If bRc then either b= c or b= c. There are cases: 1) a= b and b= c. Then a= c so aRb. 2) a= b and b= c. Then a= c so aRc. 3) a= b and b= c. Then a= c so aRc. 4) a= b and b= c. Then a= (c)= c so aRc.  
May 1st, 2017, 09:24 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,817 Thanks: 760  

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