Step 1: Understanding the Question.
An assumption is something the speaker takes for granted but never states directly. It is a statement the argument needs in order to make sense. We test each given assumption by asking whether the original statement would fall apart without it.
Step 2: Key Approach.
Use the negation test. Flip an assumption to its opposite. If the original statement then stops making sense, that assumption was implicit in it. If the statement still stands fine after the flip, that assumption was never needed and is not implicit.
Step 3: Detailed Explanation.
Assumption A says education and small family norms are directly related to the nation's progress. The statement claims that education and a small family norm "may lead the nation to progress and prosperity." This claim only makes sense if the speaker already believes there is a real link between these habits and national progress. Negate A: if education and small family norms had no relation to progress at all, the statement could never hold true. So A is a necessary, implicit assumption.
Assumption B says big families find it difficult to bear the cost of education. The original statement talks only about education and small family norms leading to progress, and says nothing about the cost of raising or educating children in big families. Negate B: even if big families did not find it hard to pay for education, the claim that education and small families drive progress can still stand on its own. B adds an idea the statement never depended on, so it is not implicit.
Step 4: Final Answer.
Only assumption A is implicit in the statement, so the correct choice is option (1), only A is implicit.