Gujarati
Hindi
2.Relations and Functions
hard

The solution set of $8x \equiv 6(\bmod 14),\,x \in Z$, are

A

$[8] \cup   [6]$

B

$[8] \cup   [14]$

C

$[6] \cup   [13]$

D

$[8] \cup   [6] \cup   [13]$

Solution

(c) $8x – 6 = 14P,\,(x \in Z)$

==> $x = \frac{1}{8}[14P + 6]$, $(x \in Z)$

==> $x$ = $\frac{1}{4}(7P + 3)$

==> $x = 6, 13, 20, 27, 34, 41, 48,.….$

$\therefore $ Solution set $= {6, 20, 34, 48,…}$ $\cup$   ${13, 27, 41, ….} $= $[6] \cup   [13]$,

where $[6], [13]$ are equivalence classes of $6$ and $13$ respectively.

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.