For i; j 2 N let (i; j) denote the ordered pair in the cartesian product N � N and fi; jg � N the
subset consisting of the elements i and j. De�ne the sets A and B as follows:
A := f;; 1; 2; (1; 3); (3; 1); f1; 3g; f3; 1gg, B := f3; (1; 2); (2; 1); f1; 2g; f2; 1; 2gg. Check whether the
following statements are true or false. Give a brief explanation for your answer.
(i): jAj = 6; (ii): jBj = 5; (iii): A \ B = ;; (iv): (3; 1) 2 A; (v): (1; 3) 2 A � B;
(vi): (3; 1) 2 A \ (B � A); (vii): (2; 1) 2 B \ (A � A); (viii): f1; 3g � A.