graphs

Question

[ D110 ; / ] = { 1,2,5,10,11,22,55,110} how are these values identified

Comments

all are the divisor of 110.

Answer 1

[D_n;/] is poset which is also a distributive lattice and it contains all divisors n.

Here n = 110 which can be written as 2¹ x 5¹ x 11¹ = (1+1) * (1+1) * (1+1) = 8 = number of divisors of 110

{1,2,5,10,11,22,55,110} these all are divisors of 110

[D₁₁₀ ; /] is also a boolean algebra.

Comments

but how do u find these 8 divisors

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prime factorization of 110 = 2 x 5 x 11 = calculate their combinations

$\binom{3}{1}$ [divisors are 2,5,11] + $\binom{3}{2}$ [divisors are 2x5 , 5x11 , 11x2] + [1,110] = 8 divisors