1. (30 points) Let E be the splitting field of 3-2 over Q. (a) Prove that E is a Galois extension of Q. (b) Use the Fundamental Theorem of Galois Theory to find |I(E/Q), where I(E/Q) is the Galois group of E over Q. = (c) Let σ,TE (E/Q) be such that σ(2) (32 and σ(3) S3 and 7(2)=√2 and T(3) 3. Find the order of σ and the order of 7 in г(E/Q). - (d) Use the Fundamental Theorem of Galois Theory to find [(()): Q), where ((a)) is the fixed field of (a). (e) Which intermediate field is ((a))?