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Show that the number of binary operation...

Show that the number of binary operations on `{1, 2}`having 1 as identity and having 2 as the inverse of 2 is exactly one.

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To show that the number of binary operations on the set \(\{1, 2\}\) having \(1\) as identity and \(2\) as the inverse of \(2\) is exactly one, we will follow these steps: ### Step 1: Define the Set and Identity Element We have a set \(S = \{1, 2\}\). According to the problem, \(1\) is the identity element. This means that for any element \(a \in S\), the following must hold: - \(a * 1 = a\) - \(1 * a = a\) ### Step 2: Create a Binary Operation Table ...
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