Let R = (x, y) : x, y ϵ Z and x2 + y2 = 25}.
Express R and R–1 as sets of ordered pairs. Show that R = R–1.
x2 + y2 = 25
Put x = 0, y = 5, 02 + 52 = 25
Put x = 3, y = 4, 32 + 42 = 25
R = {(0, 5), (0, -5), (5, 0), (-5, 0), (3, 4), (-3, 4), (-3, -4), (3, -4)}
Since, x and y get interchanged in the ordered pairs, R and R–1
are same.