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chocolatelover
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Homework Statement
(proof) Determine whether or not (x,y)~(w,z) if and only if y=w is an equivalence relation. If it is, then describe the associated partition.
Homework Equations
The Attempt at a Solution
Let x be an element of the reals. It is known that a relation on a set X is said to be reflexive if x~x for all x is an element of X. Since y and w are equal and x is an element of the reals and X is an element of the reals, this relation is reflexive.
It is known that a relaion on a set X is symmetric if for all x, y is an element of X, whenever x~y, then y~x. Since y=w, which is the same thing as saying, x~y and y~x, this relation is symmetric.
The relation is transitive if for all x, y, z is an element of X, if x~y and y~z, then x~z. It is also transitive because y=w.
Could someone please show me where to go from here?
Thank you very much
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