A binary operation is defined by m n = mn + m - n on the set of real numbers, for all m, n R. Find the value…

To solve this problem, we need to apply the given binary operation rule step by step, following the order of operations (BODMAS), which requires us to solve the expression inside the parentheses first.

1. Analyze the operation

The rule is defined as: $m \otimes n = mn + m - n$

We need to find the value of: $3 \otimes (2 \otimes 4)$

2. Solve the inner bracket: $(2 \otimes 4)$

Using the rule $m \otimes n = mn + m - n$, where $m = 2$ and $n = 4$: $(2 \otimes 4) = (2 \times 4) + 2 - 4$ $(2 \otimes 4) = 8 + 2 - 4$ $(2 \otimes 4) = 10 - 4$ $(2 \otimes 4) = 6$

3. Solve the final expression: $3 \otimes 6$

Now substitute the result back into the original expression: $3 \otimes (2 \otimes 4) = 3 \otimes 6$

Using the rule again, where $m = 3$ and $n = 6$: $3 \otimes 6 = (3 \times 6) + 3 - 6$ $3 \otimes 6 = 18 + 3 - 6$ $3 \otimes 6 = 21 - 6$ $3 \otimes 6 = 15$

4. Conclusion

Comparing our result to the options provided: A. 6 B. 25 C. 15 D. 18

The calculated value is 15, which matches option C.

Exam Tip: When dealing with binary operations involving brackets, always treat the bracketed part as a single number first. Never try to distribute the operation across the brackets, as binary operations are not always distributive!