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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