Discrete math, need translation into logic symbols and truth table / proof Steve

Question

Discrete math, need translation into logic symbols and truth table / proof

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 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. It may help to assign letters or words to propositions and use logical symbols.

Explanation / Answer

yes, it is possible to determine the relavtive salaries of Fred, Maggie and Janice.

the most paid is Fred and the least paid is Maggie.

Explanation: if we consider Fred is not highest paid then Janice should be highest paid, as the Janice is not least paid Maggie aslo should become most paid, then both Janice and Maggie will become highest paid which violates Steve's  known facts.

if Fred is highest paid then Janice will not become highest paid, at the same time Janice should become least paid because if Janice is not least paid then Maggie should become most paid which will violate Steve's known facts.

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