Read the passage below and solve these questions based on it:
A and B are two sets (for e.g., A = mothers, B = women). The elements that could belong to both the sets (for e.g., women who are mothers) is given by the set C = A × B. The elements which could belong to either set A or B or both is indicated by the set D = A ∪ B. A set that does not contain any elements is known as a null set, represented by φ (for e.g., if none of the women in the set B is a mother, then C = A × B is a null set or C = φ.
Let N signify the set of all the vertebrates; M the set of all the mammals; D the set of all the dogs; F the set of all the fish; A the set of all the alsatian and P is a dog named Party.
If P × A = φ, and P ∪ A = D, then which of the following is true?