The correct answer is (a). The vacancy of the Office of the President must be filled up within 90 days. This is according to Article 78 of the Constitution of the Philippines.
Option (b) is incorrect because the vacancy of the Office of the President must be filled up within 90 days, not 6 months.
Option (c) is incorrect because the vacancy of the Office of the President must be filled up within 90 days, not one year.
Option (d) is incorrect because the Constitution does not provide for the Parliament to determine the period within which the vacancy of the Office of the President must be filled up.