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: