A set D is countably infinite if it is in bijective correspondence with

A set S is countably infinite if it is in bijective correspondence withN, the natural numbers. An enumeration of an infinite set S is a listt(1), t(2), . . . , t(n), . . . in which each element of T occurs exactly once.Part A. Let S be a countable, infinite set and f : N → S is a bijection.Provide an enumeration of S (suggestion: use f (x) and its bijectivity) andbriefly explain why it is indeed an enumeration of S

Suppose T is an infinite set and t(1), t(2), . . . , t(n), . . . is an enu-meration of T . Show that T is countable by providing a bijection f : N →T , briefly explain why f is indeed injective and surjective

If S and T are non-empty sets. Prove that there exists a one-one correspondence(bijective) between 𝑆 × 𝑇 and 𝑇 × 𝑆

Let f be the function from{a,b,c,d} to {1,2,3,4} with f(a)=4, f(b)=2, f(c)=1,and f(d)=3,   Then  f is  bijection.Group startsTrue or FalseTrue, unselectedFalse, unselected

Let  be a function defined as . Then  is:Question 2Answera.Injective in b.Surjective in c.Bijective in d.Neither injective nor surjective in