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.

Line joining liquid phase with liquid and solid phase mixture is known as: a) liquidus b) solidus c) tie line d) none of the mentioned

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Burgers vector is generally parallel to the dislocation line. a)-true b)-false