Let * be a binary operation on the set Q of rational numbers as f… - Vidyadip

Question

Let * be a binary operation on the set Q of rational numbers as follows:
a * b = a + ab

✓

Answer

a * b = a + ab = a(1 + b) and b * a = b + ba = b(1 + a) $\neq\text{a}*\text{b}$Therefore, operation * is not commutative.
(a * b) * c = (a + ab) * c = (a + ab) + (a + ab)c
And a * (b * c) = a * (b + bc) = a + a(b + bc)
Here, $(\text{a}*\text{b})*\text{c}\neq\text{a}*(\text{b}*\text{c})$
$\therefore$ operation * is not associative.

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