# 27 of the attached Part Groups and Subgroups26. Recall that if fA Bisa one-to-one function mapping A onto B, then f(b) is the uniqeisomorphismof36isomorpi27. Prove that if :5 S' is an isomorphism of (S. *) with (S', *') and : S'→ S" is anwith (S"). then the composite function oo is an isomorphism of (S, *) with (S", *").(S) with (S,*).of binary structures, You may simply quote the results you were asked to prove in the precedingappropriate places in your proof.two exercisIn Exercises 29 through 32, give a careful proof for a skeptic that the indicated property of a binary structureis indeed a structural property. (In Theorem 3.14, we did this for the property, "There is an identity element fr29. The operation * is commutative,30. The operation is associative,31. For each c e S, the equation x *x =c has a solution x in S.32. There exists an element b in S such that b b b.fta)=b. that if : S S is an of (S, *) (S', *'), then o is i28. Prove that the of being in 3.7, is an relation on33. Let H be the subset of M20

Name: # 27 of the attached Part Groups and Subgroups26. Recall that if fA Bi
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Description: # 27 of the attached Part Groups and Subgroups26. Recall that if fA Bisa one-to-one function mapping A onto B, then f(b) is the uniqeisomorphismof36isomorpi27. Prove that if :5 S' is an isomorphism of (S. *) with (S', *') and : S'→ S" is anwith (S").