已知全集\(U=\{a_{1},a_{2},a_{3},a_{4}\}\)，集合\(A\)是集合\(U\)的恰有两个元素的子集，且满足下列三个条件：
①若\(a_{1}\in A\)，则\(a_{2}\in A\)；
②若\(a_{2}\in A\)，则\(a_{3}\in A\)；
③若\(a_{3}\in A\)，则\(a_{4}\notin A.\)
则集合\(A=(\quad)\)
A.\(\{a_{1},a_{2}\}\)
B.\(\{a_{1},a_{3}\}\) C.\(\{a_{2},a_{3}\}\) D.\(\{a_{2},a_{4}\}\)
