Q. In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication modulo $7$, if $5x = 4$, then $x =$

COMEDKCOMEDK 2010Relations and Functions - Part 2 Report Error

A

5

17%

B

4

56%

C

3

17%

D

6

11%

Solution:

$\{1, 2, 3, 4, 5, 6\}$ is a group under multiplication and 1 is the identity element
$\Rightarrow \, 5^{-1} =3$
Now, $5x=4$
$5^{-1} 5x = 5^{-1} 4 (mod 7) \Righatrrow x = 3.4$ (mod 7)
$\Rightarrow \, x=5 (mod \: 7)$

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