Let r be a relation, x a set of attributes of r, and a an attribute of r. (also, denote by xa the result of adding a to x.) define the support of x, written #x, as the number of distinct tuples in r|x (r restricted to, or projected onto, the attributes of x). prove that if x→a, then #x=#xa.

Consider a 1.2 meter high and 2 meter wide glass window whose thickness is 6 mm and thermal conductivity is 0.78 w/m °c. the room temperature is maintained at 24 °c, while the outdoor temperature is -5 °c. the convective heat transfer coefficients on the inner and outer surfaces of the window are 10 w/m2 °c and 25 w/m2 °c respectively. (a) draw the thermal resistance network, etermine the steady rate of heat transfer t e glass window (c) determine the temperature of the inner surface of the window