1. Define an appropriate function to prove that  the following sets A and B are equipotent:
   
   
• A= {1,2} B={3,4},
• A= {x ∈ N : x<7}, B is the set of weekdays,
• A is the set od even natural numbers and  B is the set of odd natural numbers.


2. Prove that the relation r defined in the set of all subsets of a set X by the formula
    
   
   A r B iff A and B are equipotent,
   
   is reflexive, symmetric and transitive.
   
   
3. Prove that the sets of all points of any two circles are equipotent.
   



4. Prove that the set A is countable (enumerable):
   
   
• A = {x ∈ N : 5|x }
• A = set of segments situated on geometric straight line and with both ending points defined in the set of rational numbers.
• A = set of circles with centre and radius in the set of rational numbers.


5. Prove that the set of points of any arbitrary circle over the plain (i.e. R² ) has  cardinality c.

 

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