How to prove that the cardinality of the Cantor Set is equivalent to the cardinality of the set of real numbers?

Determinethe cardinality of the following, including an explanation of the process

a. b. C. d. What is the cardinality of A, if A = Ø? What is the cardinality of A, if A = {a, b}? What is the cardinality of P(A), if A = {a, b}? What is the cardinality of P(A), if | A| = 5?

3. a) Do the sets {1/n:n∈N} and {1/n:n∈N}∪N have the same cardinality?  Either givean explicit bijection between them or show that no such bijection exists. Do they have the same cardinality?Proof of answer: b) Do the sets [0,1] and [0,1]∪N have the same cardinality? Either give an explicit bijection between them or show that no such bijection exists. [Hint: Part (a) will be helpful!] Do they have the same cardinality? Proof of answer: