P is saying Effective, only if Support.
It means the only correct form could be If effective, then support.
BUT Q is saying If Support, then Effective. While we know that this is not true.
Hence, Q is assuring that support will always lead to effectiveness.
(A) It simply contradicts P's claim without offering evidence against it.
--> No, He is not contradicting but using a wrong relation.(B) It does not consider the possibility that a political party might decide to support an elected legislator even though he or she ran as an independent.
--> Q is not talking about independent.(C) It fails to prove a precise definition for a key term-the word "effective."
--> come on!! This is irrelevant.(D) It presupposes what is to be proved-that a legislator must have the support of a political party in order to be "effective."
--> This is actually valid is what P is saying but Q is saying the wrong way.(E) It mistakenly interprets P to be claiming that a factor assures, rather than is necessary for, a legislator's effectiveness.
--> Correct. Support will not always mean effectiveness.