What theorem do they prove?

Question

Can the following conditional statements be arranged in logical order? If so, what theorem do they prove?
If I can't understand a problem, I get confused while studying it.
If a problem doesn't follow a pattern, then I can't understand it.
If I don't get confused while studying a problem, I can understand it.
If I get confused while studying a problem, then it is getting me trouble.
If a problem is giving me trouble, then it is too hard.

Answer 1

Just link the conclusion to the next premise.

If a problem doesn't follow a pattern, then I can't understand it.
If I can't understand a problem, I get confused while studying it.
If I get confused while studying a problem, then it is getting me in trouble.
If a problem is giving me trouble, then it is too hard.

These are now in the form:
A --> B
B --> C
C --> D
D --> E

This would imply A --> E
If a problem doesn't follow a pattern, then it is too hard.

Answer 2

1. If a problem doesn't follow a pattern, then I can't understand it.

2. If I can't understand a problem, I get confused while studying it.

3. If I get confused while studying a problem, then it is getting me trouble.

4. If a problem is giving me trouble, then it is too hard.


...If a problem doesn't follow a pattern, then it is too hard!

Answer 3

let U: I can understand a problem,
C: I get confused while studying it.
F: Problem follows a pattern.
T: Problem is giving me trouble.
H: Problem is too hard.

represent "if A then B" by A → B. we have:
1. ~U→C
2. ~F→~U
3. ~C→U
4. C→T
5. T→H

1 and 3 are equivalent contrapositives. In order:
2. ~F→~U
1. ~U→C
4. C→T
5. T→H
applying hypothetical syllogism 3 times, we get
~F→H
If the problem doesn't follow a pattern, then it is too hard.