Ex 5 Find the number of different possible colouring of points on a square using 2 colors
white and black if
a) The square is coloured on one side and the group of rotations is
G = \{R_0, R_{90}, R_{180}, R_{270}\} where R_0 = identity, R_{90} = rotation of 90 degree
counter-clockwise, R_{180} = rotation of 180 counter-clockwise, R_{270} = rotation of 270°
counter-clockwise,
b) If the group of rotation is D_4, the dihedral group of order 8