Nursing schools cannot attract a greater number of able applicants than they currently do unless the problems of low ...

I don't fully understand how answer choice E works. I understand that choice E tells us that HQHC --> PLWS or PHSS (I am writing out the contrapositive for simplicity). When we use the transitive property, we are able to conclude that HQHC --> PLWS and PHSS (I am writing out just the contrapositive for simplicity). These are not the same so I don't understand fully why E is the correct answer choice.