Let (B_{1},+,*,^{c}) is Boolean algebra where B_{1}is set of every positive dividers of 2310, in which are defined:x+y = lcm(x,y), x*y = gcd(x,y) and x^{c}= 2310/x.

Let (B_{2},∩,∪,^{c}) is Boolean algebra of every subsets of {a,b,c,d,e} with standard operations.

Let f:B_{1}→ B_{2}is isomorphism where f(2)={a} , f(3)={b} , f(5)={c} , f(7)={d} , f(11)={e}.

- How f(35), f(110), f(210), f(330) are defined?

- Determine f((30 + 5*7)^{c}).

- How many elements B_{1}have?

- Write all atoms of B_{1}.

- How many different isomorphism can be defined between B_{1}and B_{2}?

thanks for your time