Let R be a ring with ideals A and B. Define A + B = [a + b|a ∈ A, b ∈ B}. Prove that A + F is an ideal of R. (For any ring R, the ideals of R form a poset under set inclusion. If A and B are ideals of R, with glb{A, B] = A + B and lub{A, B] = A + F, the poset is a lattice.)