Answer to Question #225261 in Discrete Mathematics for Amir

Question

Find the domain and range of these functions.
i. The function that assigns to each pair of positive integers the first integer of the pair b) the
function that assigns to each positive integer its largest decimal digit
ii. The function that assigns to a bit string the number of ones minus the number of zeros in the
string
iii. The function that assigns to each positive integer the largest integer not exceeding the square
root of the integer
iv. The function that assigns to a bit string the longest string of ones in the string

Answer 1

Solution.

I. a)

Domain=$\{x|x\in N\}=\{1,2,3,4,...\}$

Range=$\{x|x\in N\}=\{1,2,3,4,...\}$

b)

Domain=

$$\{x|x\in N\}=\{1,2,3,4,...\}$$

Range=$\{0,1,2,3,4,5,6,7,8,9\}$

II.

Domain= U{0,1} * d, where d is the length of the bit string

Range=

$$\{x|x\in Z\}=\{...,-2,-1,0,1,2,...\}$$

III.

Domain=

$$\{x|x\in N\}=\{1,2,3,4,...\}$$

Range=

$$\{x|x\in Z\}=\{...,-2,-1,0,1,2,...\}$$

IV.

Domain= U{0,1} * d, where d is the length of the bit string

Range= {0,1,2,...}.