f:A→B is a partial function if Domain(f)⊆A. Number of such partial functions…
f:A→B is a partial function if Domain(f)⊆A. Number of such partial functions when ∣A∣=m and ∣B∣=n is
Answer: C. (n+1)m — Answer: (n+1)^m Explanation: A partial function from A to B may leave some elements of A undefined. For each element of A there are n possible images in B or…
- A.
nm
- B.
mn
- C.
(n+1)m
- D.
(m+1)n
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Correct answer: C
Answer: (n+1)^m
Explanation:
A partial function from A to B may leave some elements of A undefined. For each element of A there are n possible images in B or the option of being undefined, giving n+1 choices for that element.
Choices for different elements of A are independent, so multiply the choices across all m elements: (n+1) · (n+1) · … · (n+1) = (n+1)^m.
Example: if m = 2, there are (n+1)^2 partial functions, accounting for each of the two elements being mapped to one of n values or left undefined.