ISI2012-A-2c

Question

Professor Hijibiji has defined the following Boolean algebra $\mathcal{B} = (B, +, *)$, where
$B = \{1, 2, 3, 5, 6, 10, 15, 30\}$, i.e., the set of all eight factors of $30$;
the two binary operators $’+’$ and $’*’$ respectively denote the LCM (least common multiple) and GCD (greatest common divisor) of two integer operands.

Define the complementation operation $\bar{a}$ for all $a \in B$ such that $\bar{\bar{a}}= a$.

Answer 1

I think it is

  Complement of x = n / x

where n = 30 and x belongs to B.