Argument:
"Introducing mandatory coding courses in schools will significantly improve students' problem-solving abilities."
Question:
Which of the following, if true, most seriously weakens the argument?
The argument assumes that coding directly leads to improved problem-solving ability. To weaken it, we must show either that:
1. Coding does *not* improve problem-solving skills, or
2. Any observed improvement is due to some *other* factor, not coding itself.
A strong weakening statement would be:
"Studies show that students who take coding classes do not perform better on general problem-solving assessments than students who take traditional math or logic courses."
This undermines the argument by showing that coding does not uniquely or significantly enhance problem-solving skills.
Critical Reasoning -- Assumption Argument:
"Flexible working hours will increase employee productivity because people perform best during the hours when they feel most energetic."
Which of the following is a necessary assumption?
Critical Reasoning -- Strengthen Argument:
"Cities with higher public-transport usage typically experience lower air pollution levels."
Which of the following, if true, most strengthens the argument?
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: