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Let **be the binary operation on N defi...

Let `**`be the binary operation on N defined by `a ** b = HdotCdotFdot`of a and b. Is `**`commutative? Is `**`associative? Does there exist identity for this binary operation on N?

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To solve the problem, we need to analyze the binary operation defined as \( a \star b = \text{HCF}(a, b) \) where \( \star \) is the operation on natural numbers \( \mathbb{N} \). We will check if this operation is commutative, associative, and if there exists an identity element. ### Step 1: Check if the operation is commutative To determine if the operation is commutative, we need to check if \( a \star b = b \star a \) for all \( a, b \in \mathbb{N} \). - We have: \[ ...
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