In an isolated housing area consisting of 50 households, the residents are allowed to have at most one dog and at most one cat per household. Currently 25 households have a dog, 7 have both a cat and a dog, and 18 have neither a cat nor a dog. An experiment consists of randomly selecting a household and observing whether that household has a cat or a dog, or both. Using D to denote the event that the selected household has a dog and C to denote the event that the selected household has a cat, symbolically denote the following events and identify the number of households represented by each.
a The selected household has a dog but no cat.
b The selected household has a cat.
c The selected household has a cat but no dog.
d The selected household has a cat or a dog but not both.