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 April 30th, 2017, 06:39 PM #1 Newbie   Joined: Apr 2017 From: dammam Posts: 2 Thanks: 0 solve these problems Q-6 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
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Quote:
 Originally Posted by mehdi98 Q-6 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.
Are you saying you do not know what "order relation" or "ordered pairs" mean? If so where did you get this question? If you do know those definitions, you should be able to answer these questions.
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:
 b) Find the matrix representing R
What does "matrix representing R" mean?

Quote:
 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
Do you not know what an equivalence relation is? A relation is an equivalence relation if and only it satisfies
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
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Quote:
 Originally Posted by mehdi98 solve these problems ......
Is that what your teacher told YOU?

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