Determine whether each of these sets is countable oruncountable. For those that are countably infinite, exhibit a) one-to-one correspondence between the set of positiveintegers and that set.b) integers divisible by 5 and not 7c) the real numbers with decimal representationsconsisting of all 1’sd) the real numbers with decimal representationsconsisting of all 1’s or 9’s

Answer:Answers are given below.Step-by-step explanation:a) one-to-one correspondence between the set of positiveintegers and that set. Whenever we have one to one correspondence with positive integers, the set is countable and here infinite.b) integers divisible by 5 and not 7 ..This set is all integers divisible by 5 but not by 7.  This is a discrete set and hence countable and infinite.c) the real numbers with decimal representationsconsisting of all 1’s -- This cannot be counted and hence uncountable but infinite.d) the real numbers with decimal representationsconsisting of all 1’s or 9’s-- This is also uncountable but infinite.