# Set theory?

Calculus Level pending

Let $$Y^{X} \subset P(X \times Y)$$ denote the set of all functions $$f: X \rightarrow Y$$. If $$N$$ is the number of elements in $$Y^{\phi}$$ and $$M$$ is the number of elements in $$\phi^{X}$$ ($$X$$ is not empty), then what is $$N + M$$?

Details:

• $$P(K)$$ denotes the power set of the set $$K$$.
• $$\phi$$ is the empty set.
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