by 3. Let RCZ+ x Z+ be a binary relation on Z+ defined by xRy if (x mod 7 = y mod 7) And TS (Z+ xZ+)(Z+ x Z+) be a binar

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By 3 Let Rcz X Z Be A Binary Relation On Z Defined By Xry If X Mod 7 Y Mod 7 And Ts Z Xz Z X Z Be A Binar 1 (63.51 KiB) Viewed 9 times

by 3. Let RCZ+ x Z+ be a binary relation on Z+ defined by xRy if (x mod 7 = y mod 7) And TS (Z+ xZ+)(Z+ x Z+) be a binary relation on Z+ xZ+ defined (a,b)T(c,d) if a Rc and bRd (a) Prove that R is an equivalence relation on Z+. (b) Use part (a) to prove that T is an equivalence relation on Z+ x Z+. (c) Write an element from the equivalence class of (1,3). (that is; an element (c,d) such that (1,3)T(c,d)) (d) prove the following statement (you can use the quotient-remainder theorem): For all positive integers a,b,c,d: (a,b)T(c,d) + (a+b)R(c+d)