COMEDK · Maths · 17. Mathematical Reasoning
On the set \(Q\) of all rational numbers the operation * which is both associative and commutative is given by \(a * b=\)
- A \(2 a+3 b\)
- B \(a b+1\)
- C \(a^{2}+b^{2}\)
- D \(a+b+a b\)
Answer & Solution
Correct Answer
(D) \(a+b+a b\)
Step-by-step Solution
Detailed explanation
If \(a * b=b * a\), then the operation is commutative. If \((a * b) * c=a *(b * c)\), then the operation is associative. By option (d), \(\begin{aligned} &a * b=a+b+a b \\ &b * a=b+a+b a=a+b+a b \end{aligned}\) Here, \(a * b=b * a\), so the operation is commutative.…
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