Sakshi Gautam posted an Question
August 08, 2021 • 11:58 am 30 points
  • Mathematical Sciences

Example : let a be any set. let p(1) be the power set of a, that is the set of all subsetsof (csir net ma june 2 a;p (1) = {b : bc a} then which of the followi

Example : Let A be any set. Let P(1) be the power set of A, that is the set of all subsetsof (CSIR NET MA June 2 A;P (1) = {B : Bc A} Then which of the following is/are true about the set P (1) ? (1) P (A) = d for some A. (2) (3) P (A) is a countable set for some A P (A) is a finite set for some A. 3) (4) P (A) is a uncountable set for some A Solution: (2,3,4) For any set P(A) > 1 i.e., Power set P(A) is always non empty. For any finite set A with n elements |P(A)| = 2 i.e., for any finite set A, P(A) is also a finite set. If we consider the definition of a countable set as it is similar the set N then for ay y cu set A P(A)-2 =R=c i.e., for any set A,P(A) is never countably infinite. For any infinite set A, P(A) is always uncountable as above point. My question is how can power set be countable when it is not countbly infinite

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