Need some help with my discrete Mathematics Homework, converting statement

Question

Consider the following statements.

1.    1. When I work a logic example without grumbling, you may be sure it is one I understand.
2.    2. The arguments in these examples are not arranged in regular order like the ones I am used to.
3.    3. No easy examples make my head ache.
4.    4. I can't understand examples if the arguments are not arranged in regular order like the ones I am used to.
5.    5. I never grumble at an example unless it gives me a headache.
6. ∴ These examples are not easy.

Reorder the statements to explain how the conclusion follows as a valid consequence from the premises. As in Example 3.4.8, it is helpful to rewrite all of the statements in the form ∀x, if P(x) then Q(x) so that they can be easily chained together. In addition, replacing some of the premises by their contrapositives can make the connections easier to identify. (This exercise is adapted from Symbolic Logic by Lewis Carroll.†)

for the first one I thought it was if i work on a logical a statement without grumbling then i will understand,

but they want us to put it in symbolic form so I am confused

looked at example amd still confused

Answer 1

You are allowed to use the contrapositive.

So then, when Translating to english,

You can use IF and ONLY IF, and simplify/summarize

the statements.

Given premesis:

THe arguments are not in order

I grumble if and only if I do not understand,

which is equivalent to : I do not grumble iff I understand

Example is not easy if and only if I have headache

which is equivalent to: I do not have headache iff it is easy

If they are not in order then I do not understand

I grumble if it gives me a headache

The PROOF is:

The arguments are not in order

--> I do not understand

--> I grumble

--> I have headache

--> not easy