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in Sets, Relations and Functions by (20 points)
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Define binary operation on the set. Verify whether the operation * defined on Q set of rational numbers by a * b = ab belongs to Q is binary or not.

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a, b \(\in\) Q

a * b = ab

∵ If a & b are rational numbers then their multiple is also a rational number.

∴ If a.b \(\in\) Q

⇒ ab \(\in\) Q

⇒ a * b \(\in\) Q  \(\forall\) a,b \(\in\) Q

∴ operation * is binary.

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