Determine whether each statement is one-to-one and onto and prove it? (a) The fu

Question

Determine whether each statement is one-to-one and onto and prove it?

(a) The function that assigns to each pair of positive integers the maximum of these two integers. (b) The function that assigns to each positive integer the number of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 that do not appear as digits in the decimal representation of the integer. (c) The function that assigns to a binary string the numerical position of the first 1 in the string and that assigns the value 0 to a bit string consisting of all 0s.

Explanation / Answer

(a) The function is not one-one

maximum (1,3) = 3

maximum (2,3) =3

Since two sets of number map to the same number, hence the function is not one-one

The full range is covered, hence the function is onto

Therefore, the function is not one-one but onto

(b) The function will be one-one and onto

c) Function is one-one and onto

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