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Steve would like to determine the relative salaries of three coworkers using two facts. First, he knows that if Fred is not the highest paid of the three, then Janice is. Second, he knows that if Janice is not the lowest paid, then Maggie is paid the most. Is it possible to determine the relative salaries of Fred, Maggie, and Janice from what Steve knows? If so, who is paid the most and who the least? Explain your reasoning.

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Let, J = Janice , F = Fred and M = Maggie and order of salary is highest to lowest means If I write $J,F,M$ , It means J has highest salary , F has $2^{nd}$ highest and M has lowest salary.

Now, "If Fred is not the highest paid of the three, then Janice is."

It means Janice has the highest salary when Fred has $2^{nd}$ highest or lowest salary.  i.e. $J, F , M$ (or) $J, M , F$ but it is contradicting by the statement that "if Janice is not the lowest paid, then Maggie is paid the most.". So, Janice can't have the highest salary.

Now, if Fred has the highest salary then possibilities are $F,J,M$ and $F,M,J$  but $F,J,M$ is not possible because "if Janice is not the lowest paid, then Maggie is paid the most." which is contracting our assumption. So, only possibility is $F,M,J$ i.e. Fred has the highest salary , Maggie has the $2^{nd}$ highest and Janice has the lowest salary.

So, Answer is :- Relative order of salary should be Janice's salary $<$ Maggie's salary $<$ Fred's salary which means Fred is paid the most and Janice is paid the least.    

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In the Second point of what Steve knows,it's easy to determine who is paid the most and who the least if Janice is not the lowest earner.Then, Maggie is paid the most and Fred is paid the least.

In other cases,I don't think it's possible to conclude anything,even relatively.

 

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Assume, 

F: Fred is the highest paid. 
J: Janice is the lowest paid. 
M: Maggie is paid the most. 

 

Note: most indicates the greatest in quantity/number.

Translate given facts into logical statements, 

Fact 1: ($\neg$F$\rightarrow\neg$J) 

Fact 2: ($\neg$J$\rightarrow$M) 

As we know that (p$\rightarrow$q) is True for three cases (T, T), (F, T), (F, F). 

Now, we check for given facts are True by using all three cases one by one. 

Case 1: (T, T) 

fact 1: LHS:Fred is not the highest paid. RHS:Janice is the highest paid. 

fact 2: LHS: Janice is the highest paid.

in fact 2,we can't make RHS true because it's contradict with fact 1.So, Case 1 is not valid. 

Case 2: (F, T) 

fact 1: LHS:Fred is the highest paid. 

we can't make RHS true because it's contradict with LHS. So, Case 2 is not valid. 

Case 3: (F, F) 

fact 1: LHS:Fred is the highest paid. RHS:Janice is the lowest paid. 

fact 2: LHS: Janice is the lowest paid.RHS: Maggie is not the highest paid. (that means Maggie is lay between Fred and Janice because we conclude Fred is the highest and Janice is the lowest paid from fact 1.)

So, Case 3 is valid. 

Hence,the decreasing order of relative salaries is (Fred, Maggie, Janice). So, Fred is the most paid and Janice is the least paid. 

 

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It is not possible to determine the relative salaries of Fred, Maggie, and Janice from the information provided by Steve. The two facts provided are contradictory and do not provide enough information to determine the relative salaries.

If Fred is not the highest paid, then Janice is, and if Janice is not the lowest paid, then Maggie is paid the most, which creates a paradox. It is possible that either Fred or Janice could be the highest paid, and it is also possible that either Janice or Maggie could be the lowest paid, but it is not possible to determine which is which based on the information provided.

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