Group list by last 2 months and count its distinct items

List productList = new List();
class ProductTransaction
{
string product;
DateTime date_sold;
string  category;
} 
productList.Add(new ProductTransaction () {product="sword", date_sold=03/05/2017,category="weapons"});
productList.Add(new ProductTransaction() {product="sword2", date_sold=03/01/2017,category="weapons"});
productList.Add(new ProductTransaction() {product="potion", date_sold=02/05/2017,category="life"});
productList.Add(new ProductTransaction() {product="jacket", date_sold=02/03/2017,category="clothing"});
productList.Add(new ProductTransaction() {product="jacketofBear", date_sold=02/01/2017,category="clothing"});