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Let '**' be a binary operation defined o...

Let `'**'` be a binary operation defined on `NxxN` by :
`(a, b)**(c, d)=(a+c,b+d)`.
Find `(1,2)**(2,3)`.

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The correct Answer is:
To solve the problem, we need to apply the binary operation defined by the formula: \[ (a, b) ** (c, d) = (a + c, b + d) \] We are tasked with finding \((1, 2) ** (2, 3)\). ### Step-by-Step Solution: 1. **Identify the values**: - From the expression \((1, 2) ** (2, 3)\), we can identify: - \(a = 1\) - \(b = 2\) - \(c = 2\) - \(d = 3\) 2. **Apply the operation**: - According to the operation defined, we need to calculate: \[ (1, 2) ** (2, 3) = (a + c, b + d) \] - Substitute the identified values into the formula: \[ (1 + 2, 2 + 3) \] 3. **Perform the addition**: - Calculate \(1 + 2\): \[ 1 + 2 = 3 \] - Calculate \(2 + 3\): \[ 2 + 3 = 5 \] 4. **Combine the results**: - Now, we can combine the results of the additions: \[ (3, 5) \] Thus, the result of \((1, 2) ** (2, 3)\) is \((3, 5)\). ### Final Answer: \[ (1, 2) ** (2, 3) = (3, 5) \]
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