If (A) is true, that provides a reason to change library hours. But, it doesn’t provide any reason that new taxes shouldn’t be approved. (A) doesn’t connect library hours to approval of new taxes, so it doesn’t help to justify the conclusion.

(B) is a classic trap answer, because it confuses sufficiency and necessity. It tells us that if use of a public facility is made more convenient, then new taxes should be approved. But, we weren’t trying to prove that new taxes should be approved if access to libraries is made more convenient. We were trying to prove that new taxes should not be approved if access to libraries are not made more convenient. Adding (B) to the argument wouldn’t help us reach a conclusion about when new taxes should not be approved.

(C) tells us only about who should be required to pay taxes. But that doesn’t help establish that new taxes should not be approved.

(D) establishes that if we want to increase usage of public libraries, one effective strategy would be to change library hours to make them more convenient. But it doesn’t connect library hours to why we shouldn’t approve new taxes.

(E) provides a premise-to-conclusion bridge between the support – which established that most taxpayers don’t have ample opportunities to use public libraries – and the conclusion – which asserted that new taxes for libraries shouldn’t be approved. According to (E), if most taxpayers don’t have ample opportunities to use a facility (as we were told they don’t with respect to the library), then a new tax supporting that facility should not be approved.