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Let P be the set of all subsets of a giv...

Let P be the set of all subsets of a given set X. Show that `uu: P xx P->P`given by `(A , B) ->Auu B`and ` nn: PxxP ->P`given by `(A , B)->AnnB`are binary operations on the set P.

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To show that the operations of union and intersection are binary operations on the set \( P \) (the set of all subsets of a given set \( X \)), we need to verify two main properties for each operation: 1. **Closure**: The result of the operation on any two elements of the set must also be an element of the set. 2. **Definition of the operation**: The operation must be well-defined. ### Step-by-Step Solution **Step 1: Define the Set \( P \)** ...
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