cuti3panda Posted August 31, 2004 Share Posted August 31, 2004 -------------------------------------------------------------------------------- These questions are relative to Equivalence Relations.... Question[1]..Let S be the set of real number. If a,b exist in S, define a~b if a-b is an interger. Show that ~is an equivalence relation on S. Describe the equivalence classes of S. Question[2]... Let S be the set of intergers. If a,b exist in S, define aRb if ab>=0. Is R an equivalence relation on S? Question[3].. Let S be the set of interfers. If a,b exist in S, define aRb if a+b is even. Prove that R is an equivalence relation and determine the equivalence classes of S. Hints: 1]..(a,a) exist in R for all a exist in S.. [reflexive property] 2]..(a,b) exist in R implies (b,a) exist in R [symmetric property] 3]..(a,b) exist in R and (b,c) exist in R imply (a,c) exist in R [transitive property] thanks a lot Link to comment Share on other sites More sharing options...
e(ho0n3 Posted August 31, 2004 Share Posted August 31, 2004 These questions are pretty straight forward. Just show that each relation is reflexive, symmetric and transitive. If you have any specific problems, let us know. Link to comment Share on other sites More sharing options...
MandrakeRoot Posted August 31, 2004 Share Posted August 31, 2004 This is straightforward showing the three rules hold. Let me do one : a ~ a, since a -a = 0 is integer If a ~ b, then a-b is integer, hence -(a - b) = b-a is integer, thus b ~a finally if a ~b and b~c , then a - c = (a - b) - (c - b) is integer by the above and the fact that a ~b and b~c , so a ~c. IT is really easy Mandrake Link to comment Share on other sites More sharing options...
cuti3panda Posted August 31, 2004 Author Share Posted August 31, 2004 I can't figure out these problem, if you think it's easy so plzz...help me out with this...thanks a lot Link to comment Share on other sites More sharing options...
e(ho0n3 Posted August 31, 2004 Share Posted August 31, 2004 You need to help us understand what exactly you need help with. Please be specific. Mandrake already did the first question for you. Just follow Mandrake's basic outline to solve the rest of the questions. Link to comment Share on other sites More sharing options...
MandrakeRoot Posted September 6, 2004 Share Posted September 6, 2004 Say the second question, why dont you arrive to solve it ? Tell me what you tried to do in order to find the solution and maybe someone can help you find out what is missing in your argumentation ? Mandrake Link to comment Share on other sites More sharing options...
matt grime Posted September 8, 2004 Share Posted September 8, 2004 Cuti3panda, maths just follows the rules. You know what the rules are that define an equivalence relation, right? So, write them down. Now, for the second one (it isn't an equivalence relation by the way), can you try and find some where where the rules for an equivalence do not hold? It's obviously reflexive and symmetric, so what about transitive? Can you find numbers a,b,c so that ab=>0, bc=>0, but ac<0? the third one just requires you to show the rules for defining an equivlance relation are satisfied. write them out again. and write out what it means for an integer to be even (it is a multiple of two). Link to comment Share on other sites More sharing options...
cuti3panda Posted September 8, 2004 Author Share Posted September 8, 2004 Thanks a lot, matt grime Link to comment Share on other sites More sharing options...
Dave Posted September 8, 2004 Share Posted September 8, 2004 I'd also like to point out that we're not really in the habit of doing people's assignments for them Please don't just post a load of questions and expect the answers straight off; we'll hand out hints, but doing it for you is a bit cheeky and will get you in a lot of trouble if you're caught. Link to comment Share on other sites More sharing options...
MandrakeRoot Posted September 13, 2004 Share Posted September 13, 2004 I would say that the problem of doing someones exercises for them would be that they learn nothing. The whole point of such exercises (as the one above) is to get comfortable with definitions and simple application of such definitions. Mandrake Link to comment Share on other sites More sharing options...
Guest subbiahm Posted September 14, 2004 Share Posted September 14, 2004 I support Mandrakeroot.one should try in his own .That too problems of such type after solving 1 or 2 examples u should try to solve subbiah Link to comment Share on other sites More sharing options...
Dave Posted September 14, 2004 Share Posted September 14, 2004 I would say that the problem of doing someones exercises for them would be that they learn nothing. The whole point of such exercises (as the one above) is to get comfortable with definitions and simple application of such definitions. Mandrake Quite. It is extremely important to get a solid grounding in this stuff, or else you're going to be screwed when you come to the more complex stuff. Link to comment Share on other sites More sharing options...
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