Question

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

• A. [8] ∪ [6]
• B. [8] ∪ [14]
• C. [6] ∪ [13]
• D. [8] ∪ [6] ∪ [13]

Answer 1

Answer: (C)

$6$ ∪ $13$

Answer 2

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

⇒ x = $\frac { 1 } { 4 } ( 7 P + 3 )$ ⇒ x = 6, 13, 20, 27, 34, 41, 48,.......

$\therefore$ Solution set = {6, 20, 34, 48,.....} ∪ {13, 27, 41, ......}

= [6] ∪ [13].

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