Grand jury problem (LOGIC problem solving)

[einasteph29]

Hello guys..

I just want to know the answer here.
We tried to give our best just to understand this but we failed to do so..

I hope someone will help..^^

This is the problem:

Paul, Genelle, and Homer testified before a grand jury. Paul testified that Fisher did not embezzle funds only if both Laskey defrauded clients and Marshall did not receive stolen property. Genelle testified that Fisher embezzled funds and either Laskey did not defraud clients or Marshall received stolen property. Homer testified that Laskey did not defraud clients if and only if both Marshall received stolen property and Fisher embezzled funds. Based on this evidence the grand jury indicted two people. Who are they? After the indictment was handed down, it was discovered that Genelle lied. How does this affect the evidence?

Our teacher in Logic told us that we have to translate sentences in symbols then we have to make a truth-table to justify Paul's, Genelle's and Homer's statements.

Thanks in advance ^_^

 

[CompuChip]

Our teacher in Logic told us that we have to translate sentences in symbols then we have to make a truth-table to justify Paul's, Genelle's and Homer's statements.

Well, that sounds like a sensible piece of advise.
So you could start by defining
F: Fisher embezzled funds
L: Laskey defrauded clients
M: Marshall received stolen property

Then can you express the information in the story as logical statements?
For example, "If Laskey defrauded clients, then Marshall received stolen property but Fisher did not embezzle funds" would become
$$L \implies (M \wedge \neg F)$$

 

[einasteph29]

@ CompuChip:

thank u very much! ^^

 

[moonman239]

This is homework, it sounds like. The rules say you should have posted this in the homework forum.

 

[blue_raver22]

Dear fellow scientists,

Firstly, it is important to note that logic problems, such as this grand jury problem, can be challenging to solve. It requires careful analysis and application of logical principles to arrive at a conclusion. It is not uncommon for individuals to struggle with these types of problems, so do not be discouraged.

To begin solving this problem, we must first translate the given statements into symbols. Let's assign the following symbols to represent the statements:

P = Paul's statement
G = Genelle's statement
H = Homer's statement
F = Fisher embezzled funds
L = Laskey defrauded clients
M = Marshall received stolen property

Paul's statement can be translated as "not (F only if (L and not M))", which can be written as "not (F → (L ∧ ¬M))". Genelle's statement can be translated as "(F and (not L or M))", which can be written as "F ∧ (¬L ∨ M)". Homer's statement can be translated as "(not L if and only if (M and F))", which can be written as "(¬L ↔ (M ∧ F))".

Next, we can construct a truth table to analyze the statements and determine the possible combinations of true and false values for each statement. This will help us identify any contradictions or inconsistencies in the given information.

| P | G | H | F | L | M |
|---|---|---|---|---|---|
| T | T | T | T | T | T |
| T | T | T | T | T | F |
| T | T | T | T | F | T |
| T | T | T | T | F | F |
| T | T | F | F | T | T |
| T | T | F | F | T | F |
| T | T | F | F | F | T |
| T | T | F | F | F | F |
| T | F | T | T | T | T |
| T | F | T | T | T | F |
| T | F | T | T | F | T |
| T | F | T | T | F | F |
| T | F | F | F | T | T |
| T | F | F | F | T | F |
| T | F | F | F | F |