. Define a relation R on Nx N by (a, b)R(c, d) if and only if...

  

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. Define a relation R on Nx N by (a, b)R(c, d) if and only if a+b=c+d. Prove that R is an equivalence relation on N x N. Let S denote the set of equivalence classes of R. Show that there is a one-to-one and onto function from S to N. . Define a relation R on Nx N by (a, b)R(c, d) if and only if a+b=c+d. Prove that R is an equivalence relation on N x N. Let S denote the set of equivalence classes of R. Show that there is a one-to-one and onto function from S to N.

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To prove that R is an equivalence relation on NxN we need to show that it satisfies the three proper... View the full answer