# Solving a riddle using Boolean logic

• spaghetti3451
In summary, the main conflict in this scenario lies between the personal agreement between the lawyer and apprentice and the court rules. At the time the lawyer goes to court, the apprentice has not yet won her first case, so the court will rule in her favor and the lawyer will lose the case. However, after the court has made its decision, the apprentice has now won her first case and the lawyer can demand his payment again. In this scenario, the lawyer is right and will receive his payment. The importance of time is crucial in understanding the outcome of this situation.
spaghetti3451

## Homework Statement

A famous lawyer takes on an apprentice on one condition: the lawyer will train the apprentice on the business, and the apprentice will have to pay the lawyer only after she wins her first case. Right after the end of the apprenticeship, the lawyer sues his own apprentice for the amount owed.

The lawyer argues that if he wins the case, then he will be paid his due. If the apprentice wins the case, he will still get paid because she agreed to pay if she wins the first case. The apprentice on the other hand claims that if she wins then by the court's order she is no longer required to pay. On the other hand if she loses the case, then according to the original contract she is no longer obliged to pay.

Which of these two lawyers is right? Justify your answer.

## The Attempt at a Solution

Let W be the proposition "The apprentice wins her first case" and let P be the proposition "The apprentice pays her lawyer."

The apprentice will have to pay the lawyer only after she wins her first case, i.e., W$\leftrightarrow$P.

Lawyer's arguments:

1. If the lawyer wins the case, then he will be paid his due, i.e., $\neg$W→P. This does not follow from the premise.

(The court rules do not apply since the premise excludes court rules.)

2. If the apprentice wins the case, the lawyer will still get paid (because she agreed to pay if she wins the first case), i.e., W→P. This is the premise itself.

(The original agreement applies since the premise is the original agreement itself.)

Apprentice's arguments:

1. If the apprentice wins, then (by the court's order) she is no longer required to pay, i.e., W→$\neg$P. This does not follow from the premise.

(The court rules do not apply since the premise excludes court rules.)

2. If the apprentice loses the case, then (according to the original contract) she is no longer obliged to pay, i.e., $\neg$W→$\neg$P. ?

The lawyer will lose and will be paid.
When the court judges the case, the apprentice hasn't yet won any case and the lawyer loses.
However, as soon as the court has judged the case, apprentice must pay according to the contract.
Otherwise, the lawyer might sue a second time an win the case then.

I am not sure if your analysis follows the rules of discrete maths.

I am wondering if we should base our analysis of the problem only on the original payment contract or if the lawyer and his apprentice are also bound by the court rules.

In practical scenarios, informal contracts such as those agreed upon by the lawyer and his apprentice carry little weight. Court decisions overrule all such informal agreements.
However, this is a hypothetical problem in discrete maths where personal contracts could hold sway over the outcome of events.
In this regard, I am not sure if I should treat the court rules as a red herring.

I understand that the heart of the problem lies with the conflict between the personal agreement drawn out by the lawyer and her apprentice and the opposing court rules.
I simply need a clue to finish up the problem.

At the time the lawyer goes to court, the apprentice hasn't won any case yet.
Therefore, the decision of the court, in this precise case is clear: the lawyer lose the case, the apprentice wins.
After the court has decided so, then the apprentice has won his first.
From that time, the lawyer has the right to demand his due again.
He would then win if he was going to court for a second time.
Therefore, the apprentice will then have to pay.

Time is the aspect that needs to be formalized if you absolutely want to follows formal rules.
But formal rules are of no help if you miss the importance of time in this question.

Last edited:

## 1. What is Boolean logic and how does it relate to solving riddles?

Boolean logic is a system of mathematical logic that uses the values of true and false to represent logical statements. In the context of solving riddles, Boolean logic can be used to eliminate possibilities and narrow down potential solutions based on the given clues.

## 2. How do I apply Boolean logic to a riddle?

To apply Boolean logic to a riddle, you must first identify the key elements of the riddle, such as the objects, characters, and actions mentioned. Then, assign variables to represent these elements and use logical operators like AND, OR, and NOT to create statements that accurately reflect the clues given in the riddle. By evaluating these statements, you can determine the correct solution to the riddle.

## 3. What are some common logical operators used in solving riddles?

Some common logical operators used in solving riddles include AND, OR, NOT, and XOR. AND is used to represent situations where both conditions must be true, OR is used for situations where at least one condition must be true, NOT is used to negate a condition, and XOR is used to indicate that only one of the two conditions can be true.

## 4. Can Boolean logic be used to solve all riddles?

No, Boolean logic may not be applicable to all riddles. Some riddles may require more creative or lateral thinking rather than logical deduction. However, Boolean logic can be a useful tool for solving many types of riddles and can help to eliminate incorrect solutions.

## 5. Are there any tips for using Boolean logic to solve riddles?

Yes, here are a few tips for using Boolean logic to solve riddles:

• Start by identifying the key elements of the riddle and assigning variables to represent them.
• Use the given clues to create logical statements using the appropriate operators.
• Eliminate any solutions that do not satisfy all of the logical statements.
• Be sure to consider all possible combinations of logical statements and variables.
• Don't be afraid to use trial and error to test different solutions.

Replies
5
Views
2K
Replies
2
Views
2K
Replies
73
Views
9K
Replies
5
Views
6K
Replies
27
Views
3K
Replies
212
Views
13K
Replies
1
Views
1K
Replies
14
Views
3K
Replies
15
Views
4K
Replies
2
Views
18K