Does there exist a 1-1 and onto function that maps the integers to the rationales? Choose the best response below. Yes, but the function is not easily written in a "normal" way. Yes, and thus you can easily write it explicitly. No, because you can't write it explictly. No because the two set don't have the same cardinality.

Q: Let r and s be nonnegative real numbers, f(r) = r" and g(r) = r. %3D Find all pairs r and s such…

A: Given that: f(x)=xr           and             g(x)=xs

Q: Which of the following sets are countable? ORIN {7,99, 512}. 1 1 1 .}. " 10 100 1000 The set of all…

A: We know R is uncountable and N is coutable.  So, R \ N is uncountable [as R = (R \ N) U N, if R \N…

Q: Find a function whose domain is the set of all integers and whose target is the set of all positive…

A: Step:-1 Set of integers = ℤ=........-3, -2, -1, 0, 1, 2, 3,........, set of positive integers= ℕ=1,…

Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Q: Let R be the set of real numbers, A= (x € R: 5<x< 10), B = {xe R: 7<x<20), C = (0. 10], D (9, 15],…

A: