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eduhilfe
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Asked: 2020-10-05T22:45:53+01:00 In:

13. Given a non-empty set X, let \ast : P(X) \times P(X) \to P(X) be defined as A \ast B = (A-B) (B-A), \forall A, B \in P(X) . Show that the empty set \phiis the identity for the operation * and all the elements A of P(X) are invertible with A^{-1} = A. ( Hint : (A - \phi )\cup (\phi - A ) = A and (A-A)\cup (A-A) = A \ast A = \phi ).

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13. Given a non-empty set X, let \ast : P(X) \times P(X) \to P(X) be defined as A \ast B = (A-B) (B-A), \forall A, B \in P(X) . Show that the empty set \phiis the identity for the operation * and all the elements A of P(X) are invertible with A^{-1} = A. ( Hint : (A - \phi )\cup (\phi - A ) = A and (A-A)\cup (A-A) = A \ast A = \phi ).
miscellaneous-ch-1 (ncert class 12th maths)ncertrelations and functions
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