Answer
(a) The upper string will break.
(b) The lower string will break.
Work Step by Step
(a) We know that the upper string is acted upon by two forces -- that is, the downward attached weight and the second applied force. Thus, the upper string will break.
(b) We know that due to the inertia of the block, the lower string will break, if the lower string is jerked rapidly downward.