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.