Let r be the relation on n x n defined by (a, b) r(c, d) if and only if ad bc. show that r equivalence relations. is an equivalence relation on n x n.

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.