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1.1 Example Discrete Math
๐: 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. Sec-ond, 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.
๐ค: Yes, it is possible to determine the relative salaries of Fred, Maggie, and Janice based on the information provided by Steve. Here's how we can use this information:
- If Fred is not the highest paid of the three, then Janice is. This means that either Fred is second or third in terms of salary.
- If Janice is not the lowest paid, then Maggie is paid the most. This means that Maggie must be either first or second in terms of salary, with Janice being third.
Now let's consider the possible combinations of salaries for these three coworkers:
a) Fred - Second highest paid (Janice > Fred)
b) Fred - Third highest paid (Maggie > Fred > Janice)
c) Maggie - Highest paid (Janice < Maggie)
d) Maggie - Second highest paid (Fred > Maggie > Janice)
e) Janice - Lowest paid (Maggie > Janice > Fred)
From the given information, we can eliminate option e since Maggie cannot be the lowest paid if she is paid more than Janice. Therefore, the correct answer is b) Fred - Third highest paid (Maggie > Fred > Janice).
So, the relative salaries of Fred, Maggie, and Janice are:
- Fred - $X (second highest)
- Maggie - $Y (highest)
- Janice - $Z (third highest)
We don't know the exact values of X, Y, and Z, but we know their order.