Show that →, F together are expressively adequate: give sentences involving only → and F that are equivalent to ¬A, A ∨ B, and A ∧ B, respectively.
I figured out ¬A and (A ∨ B):
¬A == A → F
(A ∨ B) == (A → F) → B
But I can't figure out (A ∧ B). The closest I've come is (F → A) → B, but it does't work when A is 0/F and B is 1/T.
You can use De Morgan's Law. $$ (A \land B) \equiv \neg (\neg A \lor \neg B)$$
So, using your previous work $$(A \land B) \equiv ((A \to F) \lor (B\to F)) \to F \equiv (((A \to F) \to F) \to (B\to F)) \to F$$