The binary operation - is defined by a- b-a b 7 on the set Q of all rational numbers- Show that - is associative-

Let #160;a, #160;b, #160;c #8712;Q. #160;Then, #160;a #160;* #160;b #160;* #160;c=a #160;* #160;bc7 #160; #160; #160; #160; #1 ...

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Standard XII

Chemistry

Packing Fraction and Efficiency

The binary op...

Question

The binary operation * is defined by $a * b = \frac{a b}{7}$ on the set Q of all rational numbers. Show that * is associative.

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Solution

$Let a, b, c \in Q . Then, a * (b * c) = a * (\frac{b c}{7}) = \frac{a (\frac{b c}{7})}{7} = \frac{a b c}{49} (a * b) * c = (\frac{a b}{7}) * c = \frac{(\frac{a b}{7}) c}{7} = \frac{a b c}{49} Therefore, a * (b * c) = (a * b) * c, \forall a, b, c \in Q$

Thus, * is associative on Q.

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The binary operation * is defined by a*b=ab7 on the set Q of all rational numbers. Show that * is associative.

Let a, b, c∈Q. Then, a * b * c=a * bc7 =abc77 =abc49a * b * c=ab7 * c =ab7c7 =abc49Therefore,a * b * c=a * b * c,∀ a, b, c∈Q Thus, * is associative on Q.

The binary operation * is defined by $a * b = \frac{a b}{7}$ on the set Q of all rational numbers. Show that * is associative.

$Let a, b, c \in Q . Then, a * (b * c) = a * (\frac{b c}{7}) = \frac{a (\frac{b c}{7})}{7} = \frac{a b c}{49} (a * b) * c = (\frac{a b}{7}) * c = \frac{(\frac{a b}{7}) c}{7} = \frac{a b c}{49} Therefore, a * (b * c) = (a * b) * c, \forall a, b, c \in Q$

Thus, * is associative on Q.