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Let f: X->Y be a function. Define a r...

Let `f: X->Y` be a function. Define a relation `R` on `X` given by `R={(a ,\ b):f(a)=f(b)}dot` Show that `R` is an equivalence relation on `Xdot`

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`R = {(a,b): f(a) = f(b)}`
As `f(a) = f(a)`
`:. (a,a) in R`
`:. R` is reflexive.
If `f(a) = f(b)`
Then, `f(b) = f(a)`
Thus, `(b,a) in R`
...
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