InterviewSolution
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InterviewSolution
| 1. |
Assume that `P (A) = P (B)`. Show that `A = B` |
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Answer» Let x be an element of set A then, if `x in` then `X sub A` then, there is a subset X of set A such that `x in X` i.e., `X sub A` such that `x in A` `rArr X in P(A)` such that `x in X` `rArr X in P(B)` such that `x in X [P(A)=P(B)]` `rArr X sub B` such that `x in X` `rArr x in B " "[because x sub X and X sub B]` Therefore, `x in A rArr x in b` i.e., `A sub B` ...(1) Again, let y is any element of set B then there is a subset y of set B such that `y in Y` i.e., `Y sub B` such that `y in Y` `rArr Y in P (B)` such that `y in Y` `rArr in P(A)` such that `y in Y " "[because P(B)=P(A)]` `rArr Y sub A` such that `y in Y` `rArr y inA " "[because y in Y and Y sub A]` Therefore, `y in B rArr y in A` i.e., `B sub A` ....(2) From equations (1) and (2), A = B. |
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