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Let ** be the binary operation defined o...

Let `**` be the binary operation defined on `Q`. Find which of the following binary operations are commutative
(i) `a ** b=a-b, AA a,b in Q " " ` (ii) ` a ** b=a^(2)+b^(2), AA a,b in Q`
(iii) `a ** b=a+ab, AA a,b in Q " " ` (iv) `a ** b=(a-b)^(2), AA a,b in Q`

Text Solution

AI Generated Solution

To determine which of the given binary operations are commutative, we need to check if \( a ** b = b ** a \) for each operation. Let's analyze each operation step by step. ### Step 1: Analyze the operation \( a ** b = a - b \) 1. Compute \( a ** b \): \[ a ** b = a - b \] ...
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