Exercise 3. Let T be a set such that |T| ≥ 3 and let G = Sym(T) be the group of permutations of T. (i) For each pair a b € T, define fa,b E G by b, fa,b(t) = a, t, G|{g(a), g(b)} = {a,b}}. if t = a; if t = b; Prove that C(fa,b) = {g (ii) Prove that Z(G) = {I}. otherwise.

Asap plz handwritten solution acceptable Will definitely upvote

Let A be an atomic boolean algebra. Let X be the set of atoms. Define the map from A to p(X) as follows a > (a) f is 1-1. (b) ƒ is an isomorphism (c) f is surjective (d) f is not 1-1 {x € X : x < a}.

Show that the function is a linear transformation. Is it also an isomorphism? Upload your proofs below. Let V be the space of infinite sequences of real numbers. T(x0, x1, x2, x3, x4..) = (x0, x2, x4, ...) from V to V (we are dropping every other term) OLinear but not an isomorphism OLinear and an isomorphism ONot Linear Choose File No file chosen