Question

Let S = { 1, 2, 3, 6}.  Define x + y = lcm(x, y),  x.y = gcd(x, y) and x’ = 6/x for x, y ∈S. Show that  (S, +, . , ‘, 1, 6) is a Boolean Algebra.​

Answer 1

Answer:

for anything to be a Boolean algebra

the solution set and the original set should me same .

Step-by-step explanation:

thus LCM of any pair will belong to S

GCD of any pair will belong to S

similarly x' of any number will also belong to S .

Taking this into account we can say that the given set will be a Boolean algebra

Answer 2

Answer:

thus LCM of any pair will belong to S

GCD of any pair will belong to S

similarly x' of any number will also belong to S .

Taking this into account we can say that the given set will be a Boolean algebra

Step-by-step explanation: