Consider relation r(a, b, c, d, e) with the following functional dependencies. 1. a + b 2. e + a 3. ce → d 1. find the key(s) of r? show that the key(s) is/are minimal. 2. find a minimal basis or prove the current basis is minimal. 3. perform a bcnf decomposition of r to find a lossless-join dependency-preserving decompo- sition.

Acarnot refrigerator operates in a room in which the temperature is 21°c and of power when operating. if the food compartment of the refrigerator is consumes 3 kw to be maintained at 2°c, determine (a) the coefficient of performance of the cycle and (b) the rate of heat removal from the food compartment. refrigerator cycle that has a higher coefficient of performance than that of the discussed (e) is it possible to develop a carn ot refrigerator, operating between the same temperature limits? explain