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Let A be set of 4 elements. From the set of all functions from A to A, a function is chosen at random. The chance that the selected function is an onto function is
- a)3/32
- b)29/32
- c)1/64
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Let A be set of 4 elements. From the set of all functions from A to A,...
Solution:
An onto function is one which maps every element of the domain to a unique element of the range, i.e., every element of the range is associated with at least one element of the domain.
Number of all functions from A to A = 4^4 = 256
Number of functions which are not onto = (4-1)^4 = 81
(For every element in the range, there are 3 ways to choose an element from the domain such that it is not mapped to that element.)
Therefore, number of onto functions = 256 - 81 = 175
Probability of selecting an onto function = 175/256
Hence, the answer is option A.
An onto function is one which maps every element of the domain to a unique element of the range, i.e., every element of the range is associated with at least one element of the domain.
Number of all functions from A to A = 4^4 = 256
Number of functions which are not onto = (4-1)^4 = 81
(For every element in the range, there are 3 ways to choose an element from the domain such that it is not mapped to that element.)
Therefore, number of onto functions = 256 - 81 = 175
Probability of selecting an onto function = 175/256
Hence, the answer is option A.
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Let A be set of 4 elements. From the set of all functions from A to A, a function is chosen at random. The chance that the selected function is an onto function isa)3/32b)29/32c)1/64d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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