My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree1Thanks
  • 1 Post By Country Boy
Reply
 
LinkBack Thread Tools Display Modes
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
mehdi98 is offline  
 
May 1st, 2017, 09:14 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,649
Thanks: 681

Quote:
Originally Posted by mehdi98 View Post
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.
Thanks from greg1313
Country Boy is offline  
May 1st, 2017, 09:24 AM   #3
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 10,471
Thanks: 693

Quote:
Originally Posted by mehdi98 View Post
solve these problems
......
Is that what your teacher told YOU?
Denis is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
itif, problems, solve, solving, trouble



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Please Solve this 4 EPIC Problems.... i couldn't solve it myself gen_shao Algebra 12 November 2nd, 2014 06:11 AM
How to master maths - should we solve simple problems or variety of problems? joshis1 Algebra 2 October 10th, 2014 03:55 PM
Can somebody help solve this problems please vloraboy Algebra 3 April 2nd, 2009 01:05 PM
Need help to solve few problems :( amero Calculus 3 August 14th, 2008 10:54 AM
CAN SOMEBODY HELP SOLVE THIS PROBLEMS PLEASE vloraboy Abstract Algebra 0 December 31st, 1969 04:00 PM





Copyright © 2017 My Math Forum. All rights reserved.