Question

1. A nuclear power plant has double redundancy on the feedwater pumps used to remove heat from the reactor core. A safely operating plant requires only one of the three pumps to be functional. Define the events A, B, and C as follows: A: Purup I works properly B: Pump 2 works properly C: Pump 3 works properly Describe in words the following events (a) The intersection of A, B, and C (b) The union of A, B, and C (c) The complement of the intersection of A, B, and C (d) The complement of the union of A, B, and C

Answer 1

(a)

The intersection of A,B and C is the intersection of the events of Pump 1 working properly, Pump 2 working properly and Pump 3 working properly. Thus it is the event that all the three pumps 1,2 and 3 are working properly. Thus the plant is operating safely in this event.

(b)

The union of A,B and C is the union of the events of Pump 1 working properly, Pump 2 working properly and Pump 3 working properly. Thus it is the event that atleast one of the three pumps 1,2 and 3 are working.Thus the plant is operating safely in this event.

(c)

The complement of the intersection of A,B and C is the complement of the event in Part(a) . Thus it is the event that no all 3 Pumps are working properly. Thus it is the event that atmost two Pumps are working properly. The plant may or may not be working safely under this event.

(d)

The complement of the union of A,B and C is the complement of the event in Part(b). Thus it is the event which is the opposite of atleast one Pump working properly. Thus it is the event that no Pump is working properly. Thus the plant is not operating safely in this event.