Step 1: Understand the given statement.
The statement says that private tutoring is both effective and fun. It does not make any general claim about all teaching methods, nor does it explain how private tutoring is conducted.
Step 2: Examine Assumption 1.
Assumption 1 claims that all effective methods of teaching children are also fun. The given statement talks only about private tutoring and does not generalize effectiveness and fun to all teaching methods. Hence, this assumption is not implicit.
Step 3: Examine Assumption 2.
Assumption 2 states that private tutors typically use visual aids. The statement does not mention any teaching tools or methods such as visual aids. Therefore, this assumption is also not implicit.
Step 4: Conclusion.
Neither of the given assumptions is necessary for the statement to be true. Hence, both assumptions are invalid.