Determine whether each of the following statements is true or false. For each false statement give a counterexample.
(a) If (/?, +, •) is a ring, and 0 ≠ S ⊂ R with S closed under + and ∙, then S is a subring of R.
(b) If (R, +, •) is a ring with unity, and S is a subring of R, then S has a unity.
(c) If (R, +, •) is a ring with unity uR, and S is a subring of R with unity us, then uR = us,
(d) Every field is an integral domain.
(e) Every subring of a field is a field.
(f) A field can have only two subrings.
(g) Every finite field has a prime number of elements.
(h) The field (Q, +, •) has an infinite number of subrings.