Palle and Jens are looking at which capitals they have visited. Palle has visited 17 capitals, whereas Jens has visited 23. The number of capitals visited by at least one of them is 33.

(a) How many capitals have been graced by a visit from both?

(b) Call Palle’s capitals P, and Jens’ capitals J. How do you write “capitals visited by at least one of the two”?

(c) How do you write the set of capitals visited by both?

(d) Recall that the cardinality (size) of the set A is |A|.Write a formula to link the cardinalities of the sets in the previous two exercises and those of P and J themselves.