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Math Help - equivalence class

  1. #1
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    equivalence class

    Let S be the Cartesian coordinate plane RxR and define a relation R on S by (a,b)R(c,d) iff a+d=b+c. Verify that R is an equivalence relation and describe the equivalence class E(7,3).
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by yenbibi View Post
    Let S be the Cartesian coordinate plane RxR and define a relation R on S by (a,b)R(c,d) iff a+d=b+c. Verify that R is an equivalence relation
    you must show three things. R is reflexive, symmetric and transitive

    (a) Reflexive: you must show that (a,b)R(a,b) for all (a,b) \in \mathbb{R} \times \mathbb{R}

    (b) Symmetric: you must show that (a,b)R(c,d) \implies (c,d)R(a,b) for (a,b), (c,d) \in \mathbb{R} \times \mathbb{R}

    (c) Transitive: you must show that \Bigg[ (a,b)R(c,d) \mbox{ and } (c,d)R(e,f) \Bigg] \implies (a,b)R(e,f) for (a,b), (c,d), (e,f) \in \mathbb{R} \times \mathbb{R}


    can you do that?


    and describe the equivalence class E(7,3).
    what do you mean E(7,3)? you mean the equivalence class that has the point (7,3) in it?
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  3. #3
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    Quote Originally Posted by Jhevon View Post

    what do you mean E(7,3)? you mean the equivalence class that has the point (7,3) in it?
    Yes, and we can write it as \overline{(7,3)}=[(7,3)].
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    Yes, and we can write it as \overline{(7,3)}=[(7,3)].
    in that case, it is just [(7,3)] = \{ (a,b) \mid 7 + b = 3 + a \Longleftrightarrow a - b = 4 \}
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