Answer:
X = {8n – 7n – 1 : n ϵ N}
Y = {49 (n –1) : n ϵ N} — (1) [all terms divisible by 49]
X = {8n – 7n – 1}
= (1 + 7)n – 7n – 1
= 1 + nC1 7 + nC2 72 + ….. + nCn 7n – 7n – 1
= nC2 72 + …… + nCn 7n
= 49 [nC2 + nC3 7 + …. nCn 7n-2] — (2)
From (1) and (2),
X is divisible by 49.
Y has all multiples of 49.
X ⊂ Y
The decimal form is 1.3 (3 repeating) and the simplified form is 1 14/45
