Let A and B be Boolean algebras and f: A → B is an isomorphism, and A is atomic.
(a) B is atomic, (b) B is complete (c) A is atomless (d) B is atomless
I think the answer is (A) by the representation theorem
edit:
also, I found similar questions online
Let A and B be Boolean algebras and f : A → B is an isomorphism, and A is complete.
(a) B is atomic, (b) B is complete (c) A is atomless (d) B is atomless
Let A and B be Boolean algebras and f : A → B is an isomorphism, and A complete and atomic
(a) B is complete and atomic, (b) B is finite (c) A is atomless (B) is atomless
The answer is $A$ because isomorphisms preserve the BA structure, so images of atoms are atoms etc. Not because of a representation theorem.