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Define a Relation TT On R\mathbf { R } As Follows: for All

question 11

Essay

Define a relation TT on R\mathbf { R } as follows: for all xx and yy in R,xTy\mathbf { R } , x T y if and only if x2=y2x ^ { 2 } = y ^ { 2 } . Then TT is an equivalence relation on R\mathbf { R } .
(a) Prove that T is an equivalence relation on R.
(b) Find the distinct equivalence classes of T.

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