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  4. In the group G = 1, 5, 7, 11 under otimes12 the value of 7 otimes12 11-1 is equal to

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Q. In the group $G = \{1, 5, 7, 11\}$ under $\otimes_{12}$ the value of $7 \otimes_{12} 11^{-1}$ is equal to

COMEDKCOMEDK 2012Relations and Functions - Part 2

Solution:

$G = \{1, 5, 7,11\}, \oplus_{12}$
we know that 1 is an identity element.
inverse of 11 is,
$11 \oplus_{12} 11^{-1} = 1$ and $11 \oplus_{12} 11 = 1$
Hence $11^{-1} = 11. \therefore \, 7 \oplus_{12} 11^{-1} = 7 \oplus_{12} 11 = 5$