The exercise is a puzzle that can be solved by translating Statements into logical expressions and reasoning from these expressions using truth tables. 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.

SOLUTIONStep 1We have to solve the given puzzle by translating statements into logical expressions .Step 2Given 1 )If Fred is not the highest paid of the three, then Janice is.2) If Janice is not the lowest paid ,then Maggie is paid the most.We have to find, who is paid the most and who is paid the least.Step 3Consider the following logical expressionsp : Fred is paid the mostq: Maggie is paid the most r:Janice is paid the mosts:Janice is paid the leastStep 4If Fred is not the highest paid of the three, then Janice, is expressed as, If Janice is not the lowest paid ,then Maggie is paid the most, is expressed as,Next find the corresponding truth table Step 5 p q r s(F FTFTFFF TFTFTFT FFTTTTF TFFFTFTFF FTFFConsidering the truth values of each statements , we conclude that,Fred is paid the most and Janice is paid the least.Therefore the order is Fred >Maggie>Janice.