Question

Which one of the following three sets is a reduced residue system modulo 8?

A: {1,2,3,5,7}

B: {1,3,5,7}

C: {2,3,5,7}

D: {1,3,5,8}

Answer 1

option B

Explanation:

The reduced residue system modulo is the set for a number in which greatest common divisor is 1 for the set of the number from the set and the number belonging to residue system modulo

for the given problem,

g.c.d(n,8) = 1,

here, n is the number from the set

thus, for the option B {1, 3, 5, 7}

for, n = 1

g.c.d(1,8) = 1,

for, n = 3

g.c.d(3,8) = 1,

for, n = 5

g.c.d(5,8) = 1,

for, n = 7

g.c.d(7,8) = 1,

hence, for every 'n' belonging to the set given in the option B satisfies the condition

hence, option B is correct