In all the problems below F is an extension field of K 1. Prove (a) [F: K] 1 if and only if FK (b) If [F: K] is prime and E is an intermediate field, then E = K or E = F (c) If u F has degree n over K, then n divides [F: K] 2. If F is algebraic over K and R is a subring of F with KCRCF, show that R is a field. 3. Prove that every element of K(r) that is not in K is transcendental over K.