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Given a none-empty set X,let∗:P(X)×P(X)→P(X) be defined as A×B=(A−B)∪(B−A),∀A,B∈P(X). Show that the empty set ϕ is the identity for the operation ∗ and all the elements A of P(X) are invertible with A−1=A. |
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Answer» Given a none-empty set X,let∗:P(X)×P(X)→P(X) be defined as A×B=(A−B)∪(B−A),∀A,B∈P(X). Show that the empty set ϕ is the identity for the operation ∗ and all the elements A of P(X) are invertible with A−1=A. |
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