oneto One Correspondence b Describe a onetoone correspondenc

one-to One Correspondence:

b. Describe a one-to-one correspondence between the set of positive integers and the set of perfect cubes (1, 8, 27, 64, 125, …)

c. Describe a one-to-one correspondence between the points on a line of length 1 inch and the points on a line of length 3 inches.

d. Describe a one-to-one correspondence between the points on a line of length 1 inch and the points on a line of length 100 miles.

Solution

one-to-one correspondence from a set A to set B is a function from A to B so that no two distinct elements in A map to the same element in B

b. Required map is: f(n)=n^3

c. Represent the points on the x axis extending from x=0 to x=1

Required map is:g(x)=3x

d.

Represent the points on the x axis extending from x=0 to x=1

100 miles =6336000=k

So the required map is:h(x)=kx