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 7
c) the real numbers with decimal of all 1’s
d) the real numbers with decimal of all 1’s or 9’s

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 of all 1’s

-- This cannot be counted and hence uncountable but infinite.

d) the real numbers with decimal of all 1’s or 9’s

-- This is also uncountable but infinite.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.