Biology, asked by sandhya849092, 1 year ago

Let P be the set of all subsets of a given set X. Show that ∪ : P × P → Pgiven by (A, B) → A ∪ B and ∩ : P × P → P given by (A, B) → A ∩ B are binaryoperations on the set P.

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Solution :Since union operation ∪ carries each pair (A, B) in P × P to a unique elementA ∪ B in P, ∪ is binary operation on P. Similarly, the intersection operation ∩ carrieseach pair (A, B) in P × P to a unique element A ∩ B in P, ∩ is a binary operation on P.

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Let P be the set of all subsets of a given set X. Show that ∪ : P × P → Pgiven by (A, B) → A ∪ B and ∩ : P × P → P given by (A, B) → A ∩ B are binaryoperations on the set P.​

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Let P be the set of all subsets of a given set X. Show that ∪ : P × P → Pgiven by (A, B) → A ∪ B and ∩ : P × P → P given by (A, B) → A ∩ B are binaryoperations on the set P.