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few more tough questions?
1) show that the identity element in a group is unique. prove that the inverse on any given element in a group is unique
2) Define a power set
3) state the three problems of antiquity and in what sense has each of these been solved
1 Answer
- WillLv 51 decade agoFavorite Answer
1. Suppose it wasn't. Then there exists distinct a,b such that for all x xb=x and xa=x. Then ab=a, as b is the identity, and ab=b as a is the identity. Therefore, a=b. Contradiction distinct. Proof for inverse is the same pretty much. Suppose that k had two inverses, c and d. Then kc=e and kd=e, then kc=kd, then c=d.
2. Power set is the set of all subsets. EG. if S = {1,2} P(S) = { empty set, {1},{2}.{1,2} } where P(S) is pronounced "the power set of S"
3. You're on your own on that one. Probably something your teacher talking about in class or that's discussed in your book.