Let us see statements one by one ..
Statement 1 is true as if we add some row to a table of the 2 tables in the join , so cross product will occur first after then selection of records based on common attribute value and then projection of irredundant attributes..So in worst case the records resulting from new tuples in the cross product will not be selected(possibly due to the fact the common attribute value is not common to both tables hence not going to be included else included)..Thus in any case the result of join will not diminish..Hence natural join is monotone..
Statement 2 which says intersection is monotone is also true..Because in worst case scenario the record added is not common to both hence will not come in the result.But original result of intersection will remain the same as exisitng tuples are not deleted..
Statement 3 is false because say we have 2 tuples A and B ..So say we have some tuple added to B which is part of A also so the difference result will get diminished as that tuple will not come in A - B further..Hence difference operator is not monotone..
Statement 4 is true because selection operator will select the desired tuples of original relation plus those new tuples which are satisfying selection condition as well(if any)..hence it is monotone also..
Hence A) , B) and D) are monotonous operators..
