Let A 1 2 3 6 12 18 and R be defined by xRy if and only if

Let A = {1, 2, 3, 6, 12, 18} and R be defined by xRy if and only if x|y.
1) Give a subset of B of A that is linearly ordered with respect to R and contains at least three elements.
Please explain answer.

Solution

xRy iff X/Y

subset b of a which is linearly ordered with xRy

will be {1,2,3,6}

because 1/2 , 2/6, 3/6, 6/12

xRy also fullfill this condition hence ordered.