From proposition ①: a=b2+ 1.
→④
From proposition 2, we can get: 3 = a+b.
→⑤
From proposition ③: 0=4a+2b→⑥
If ① is a true proposition, then a=b2+ 1, that is, Equation ④ is an identity.
Substitute ④ into ⑤ and you will have a solution. Explain that ⑤ can be established, that is, proposition ② is true.
Substitute ④ into ⑥, and there is no solution. Explanation 6 cannot be established, that is, proposition 3 is false.
So choose the answer of "proposition 2 is true and proposition 3 is false", that is, option C.