doubt

Question

C intersection P(C) != phir ?why?

(phi is subset of every set)???

Answer 1

C is a set such that C={a, {a}}

P(C)= {{ }, {a}, {{a}}, {a,{a}}}

Now, C Intersection P(C) = {a} which is not empty set, hence above statement is correct.

Comments

By default , { } is subset of every set // Is a a wrong statement ?

bcz according to this statement , {} is subset of C and P(C) .

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You didn't interpret the question correctly! they are not asking about the subset, but they are asking about the resulted set after intersection operation.

Yes, { } is subset of each set, is a correct statement.

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{ } is subset of each set.Then

C={a, {a}} is equivalent to  C={{},a, {a}}

NOw,

P(C)=    { {} ,{{ }}, {a}, {{a}}, ......

NOw, C intersection P(C) is phi ?

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C={a, {a}} is equivalent to  C={{},a, {a}}

Both are not equivalent as first set has 2 members and second set has 3 members.

What all i can suggest you is, that you must read set theory from Keneath Rosen and solve given exercises in the book.