Consider the non empty sets A and B such that A and B have the same cardinality. Prove, for any set C, that the sets A x B and B x C have the same cardinality

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:

Consider two sets A and B defined in the universal set U. Set A contains elements that are prime numbers less than 20, and set B contains elements that are multiples of 3 less than 20. Define set C = A ∪ B (the union of A and B), and set D = A ∩ B (the intersection of A and B). Find the power set of D.

Do the sets [0,1] and [0,1/2)∪(1/2,1] have the same cardinality? Either give an explicit bijection between them or show that no such bijection exists