1. Show that the relation R in the set N of Natural numbers given by R = {(a,b): |a-b| is a multiple of 3} is an equivalence relation.
Determine whether each of the following relations are reflexive, symmetric, and Transitive.
2. Check whether the relation R in R defined by R = {(a,b):a< b3} is reflexive, symmetric, transitive.
3. Prove the relation R on the set N x N defined by (a, b) R (c,d)↔ a+d = b + c, for all (a, b) (c, d) є N x N is an equivalence relation.
4. Prove that the function f: R →R, given by f (x) = |x| + 5, is not bijective.
5. Prove that the function f: R→R, given by f (x) =4x3 -7, is bijective
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