The question is in the form of a disjunctive syllogism- Either A or B
The conclusions that follow are Not A, therefore B
And Not B, therefore A
Here the options are either a maid or a cook.
If a maid is not employed, a cook is employed.
If a cook is not employed, then a maid is employed and also if a cook is not employed, she will change her job.
Hence if a maid is employed, she changes her job is correct.
Hence option E is the correct answer.