2,697 views
3 votes
3 votes
Let A and B be countably infinite set which of the following is false :-

a.) any subset of a or b is countable infinite

b:) A union B and A*B is countable infinite

c:)the union of countable infinite collection of countably infinite sets is countable infinite

d)cartesian product of countable infinite collection of countable infinite sets is countable infinite

2 Answers

2 votes
2 votes

its simple, as it says.

=> any subset of A or B is countable infinite (given that A and B are countably infinite)

so consider the empty set{} 

since we know that every empty set ∅ is a subset of any set and we can say that an empty set has no elements means 0 element

so that means its countable.

so option A is false..

now coming to options b,c,d all are COUNTABLY INFINITE.

For finding A union B (say A denotes all natural odd numbers which is countably infinite so as B that denotes all natural even numbers) and their union is all natural numbers set (which is countably infinite)

for finding cartesian product let A and B both denotes sets of all even natural numbers now A*B = {aRb | (a+b ) sum of all even numbers and whose sum is >=4 which is also countably infinte}.

Related questions

2 votes
2 votes
2 answers
2
Atul Sharma 1 asked Aug 26, 2018
1,861 views
A language in NOT - RE is un-countably infinite. true or false?
1 votes
1 votes
1 answer
3
1 votes
1 votes
0 answers
4
sanket03 asked Dec 18, 2018
179 views
Can someone tell me if countability topic from toc is still in syllabus of gate 2019 or not