The problem with this question is I don't quite understand it, or rather how to think about the question. It's a multiple choice question and below are a couple of the options:
(a)
- $T = \{n|n>0$ and $n|8\}$
- $x\land y = $ gcd$(x,y)$
- $x\lor y = $ lcm$(x,y)$
- $x' = 8/x$
- Zero $= 1$
- One $= 8$
(b)
- $T = \{n | n>0$ and $n|30\}$
- $x\land y =$ gcd$(x,y)$
- $x\lor y =$ lcm$(x,y)$
- $x' = 30/x$
- Zero $= 1$
- One $= 30$
These are just two of the options but how do I know if (a) or (b) can be used to define a Boolean algebra?