18(a)

(b)

19(a)

(b)

20(a)
(b)

0800MAT203122001

Solve the recurrence relation ‏جہہہه‎ — 40141 + 3a, = —200,n > 0,

‎a, = 3300‏ ,3000 = مه

‎Solve the recurrence relation a, = 2൨൮ — 4८1 -2 ,7} = 3,a, = 2,a, = 0
Module 5

‎If f:(R*,°) > (R, +) as f(x) = മാം where R* is the set of positive real

‎numbers. Show that ரீ is a monoid isomorphism from R* onto R.

‎Show that every subgroup of a cyclic group is cyclic.

‎State and prove Lagrange’s Theorem.

‎If A = {1,2,3}. List all permutations on A and prove that it is a group.

‎Page 3 of 3

‎(6)

‎(8)

‎(6)

‎(8)
‎(6)

‎(8)