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- Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a set A into itself such that fg=fh and gh.Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .
- 8. a. Prove that the set of all onto mappings from to is closed under composition of mappings. b. Prove that the set of all one-to-one mappings from to is closed under composition of mappings.Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg, then f=h. b. Prove that if f is one-to-one and fg=fh, then g=h.True or False Label each of the following statements as either true or false. The set of all bijections from A to A is closed with respect to the binary operation of composition defined on the set of all mappings from A to A.