The correct answer is Option 4: A is false but R is true.

Let`s analyze each option for better understanding.

Option 1 states that both A and R are individually true and R is the correct explanation of A. This is incorrect because while R is true, A is not. Maulana Mohammad Ali and Abul Kalam Azad did not resign in 1916.

Option 2 states that both A and R are true but R is not the correct explanation of A. This is also incorrect. While R is true, A is not and thus, R cannot explain A.

Option 3 is incorrect as it states that A is true but R is false. A is false, but R is true. The Rowlatt Act, which allowed certain political cases to be tried without juries and permitted internment of suspects without trial, was indeed passed without the support of Indian members in the legislature.

Option 4 suggests that A is false but R is true, which is indeed correct. Maulana Mohammad Ali and Abul Kalam Azad did not resign from the Legislative Council in 1916, and the Rowlatt Act was passed despite opposition from Indian members. Therefore, Option 4 is correct.