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Pingunoot
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Let X = R × R. Define the relation R on X as follows:
(x1 , y1 )R(x2 , y2 ) iff y1 − y2 = 2(x1 − x2 ).
(a) Is it an equivalence relation?
(b) If it is, what is the equivalence class of the point (3, 1)?
I've proved this for reflexive, but I'm not sure how to go about doing it for symmetric and transitive and finding the equivalence class :S
Any guidance would be much appreciated :)
Please note, homework assignments or textbook style exercises for which you are seeking assistance are to be posted in the appropriate forum in our https://www.physicsforums.com/forumdisplay.php?f=152" area. This should be done whether the problem is part of one's assigned coursework or just independent study.
Let X = R × R. Define the relation R on X as follows:
(x1 , y1 )R(x2 , y2 ) iff y1 − y2 = 2(x1 − x2 ).
(a) Is it an equivalence relation?
(b) If it is, what is the equivalence class of the point (3, 1)?
I've proved this for reflexive, but I'm not sure how to go about doing it for symmetric and transitive and finding the equivalence class :S
Any guidance would be much appreciated :)
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