The correct answer is Option 2: Both I and II.

Option 1: "Neither I nor II" is incorrect because both statements I and II are clearly stated in the Constitution of India. Statement I mentions that the President cannot be a member of either House of Parliament, as per Article 59(1). Statement II states that the Parliament consists of the President and two Houses - the Rajya Sabha (Council of States) and the Lok Sabha (House of the People), as described in Article 79.

Option 3: "I alone" is incorrect because while it correctly outlines that the President cannot be a member of either House of Parliament, it ignores the second statement, which is also a fact as per the Indian Constitution.

Option 4: "II alone" is wrong as it overlooks the first statement which is equally apt per the Constitution.

Therefore, Option 2: "Both I and II" is correct as it completely abides by the facts stated in the Constitution of India.