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Let A be a denumerable set. Determine, with explanation, whether each of the following
Chapter 5, Problem 11(choose chapter or problem)
Let A be a denumerable set. Determine, with explanation, whether each of the following is true or false. (a) The set of 0-element subsets of A is countable. (b) The set of 1-element subsets of A is countable. (c) The set of 2-element subsets of A is countable. (d) The set of all subsets of A is countable.
Questions & Answers
QUESTION:
Let A be a denumerable set. Determine, with explanation, whether each of the following is true or false. (a) The set of 0-element subsets of A is countable. (b) The set of 1-element subsets of A is countable. (c) The set of 2-element subsets of A is countable. (d) The set of all subsets of A is countable.
ANSWER:Step 1 of 5
A set is called denumerable if it has the number of elements, same as the set of positive integers. A finite set or denumerable set is always countable. A denumerable set can also be defined as countable infinite.