See the attached truth tables.
• A ∧ B is true only when both A and B are true
• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B
• ¬A is true only when A is false
• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)