Correct: The picture is consistent with the preferences being strictly
monotone.
False: The picture is consistent with the preferences being convex.
Explanation:
All the indifference curves that are shown are downward sloping. If this
property holds for all indifference curves and if elements on
indifference curves further north east are ranked higher, then the
preferences are indeed strictly monotone. Thus the picture is consistent
with the preferences being strictly monotone.
To show that the picture precludes the possibility of the underlying
preferences being convex, suppose first that the preference are strictly
monotone (the proof can be generalized to not assuming that) and
consider the points A,B,C and D below: