KCET · Maths · Mathematical Reasoning
On the set of all natural numbers \(N\), which one of the following * is a binary operation?
- A \(\mathrm{a} * \mathrm{~b}=\sqrt{\mathrm{ab}}\)
- B \(a * b=\frac{a-b}{a+b}\)
- C \(a * b=a+3 b\)
- D \(a * b=3 a-4 b\)
Answer & Solution
Correct Answer
(C) \(a * b=a+3 b\)
Step-by-step Solution
Detailed explanation
Since, \(a, b \in N\),
\[
\therefore \quad \mathrm{a} * \mathrm{~b}=\mathrm{a}+3 \mathrm{~b} \in \mathrm{N}
\]
Hence, option (c) is correct.
\[
\therefore \quad \mathrm{a} * \mathrm{~b}=\mathrm{a}+3 \mathrm{~b} \in \mathrm{N}
\]
Hence, option (c) is correct.
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