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taurus [48]
3 years ago
11

Let a, b, c and x elements in the group G. In each of the following solve for x in terms of a, b, and c.

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

Answer:

x=c.a^{-1}.b^{-1}

Step-by-step explanation:

Given equation,

axb = c-----(1)

(axb) ( a^{-1}.b^{-1} ) = c.(a^{-1}b{-1})

(xb)(a)(a^{-1}.b^{-1} ) = c.(a^{-1}b{-1}) ( commutative law of multiplication )

(xb)(a.a^{-1}).b^{-1} = c.a^{-1}b{-1} ( Associative property )

(xb).e.b^{-1} = c.a^{-1}b{-1}

(xb).b^{-1}=c.a^{-1}.b^{-1}   ( identity property )

x.(b.b^{-1})=c.a^{-1}.b^{-1}  ( Associative property )

x.e=c.a^{-1}.b^{-1}      

x=c.a^{-1}.b^{-1}                 ( identity property )

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