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spaghetti3451

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## 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.

## Homework Equations

## 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[itex]\leftrightarrow[/itex]P.

Lawyer's arguments:

1. If the lawyer wins the case, then he will be paid his due, i.e., [itex]\neg[/itex]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→[itex]\neg[/itex]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., [itex]\neg[/itex]W→[itex]\neg[/itex]P. ?

Please help me out!