IF P(A)=P(B) SHOW THAT A=B

A+B

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Let x be an elemets of A so there exist a subset called X such as x belongs to X so

X will be subset of A=> X belongs P(A)

 Xbelongs to P(B)

  X wiill be subset of B

 x belongs to A => x belongs to B

A ill be subset of B

similarly B will be subset of A

 

SO WE GET A=B

  HENCE PROVED

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let X belongs to A

X subset of A

XCA=>X belongs to P(A)

=>X belongs P(B)        (...P(A)=P(B) )

=>X subset of B=>X belongs to B

X belongs to A =>X belongs to B   . .. A subset of B (1)

similarly through the same steps,

Y belongs to B=>Y belongs to A   ...B subset of A(2)

From (1)&(2)A=B

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