kazu3273

Please explain how to solve the following questions,

1) Let p and q be distinct primes. THere is a proper subgroup J of the
additive group of integers which contains exactly three elements of
the set {p,p+q,pq,p^q,q^p}. Which three elements are in J?

(A) pq, p^q,q^p
(B) p+q, pq, p^q
(C) p,p+q,pq
(D) p,p^q,q^p
(E) p,pq, p^q

2) An automorphism phi of a field F is a one-to-one mapping of F onto
itself such that phi(a + b) = phi(a) + phi(b) and phi(ab) =
phi(a)phi(b) for all a, b in F. If F is the field of rational numbers,
then the number of distinct automorphisms of F is
(A) 0
(B) 1
(C) 2
(D) 4
(E) infinite