How to express an if and only if statement using ∧, ∨, and ¬?

Question

Say I have a statement A if and only if B. How do I do it without an arrow just using these symbols? Do I get a truth table? Thank you.

Answer 1

$A \Rightarrow B$ is the same as $¬A ∨ B$

$B \Rightarrow A$ is the same as $¬B ∨ A$

So...

$$A \Leftrightarrow B$$ is the same as $(¬A ∨ B) ∧ (¬B ∨ A)$

Answer 2

Also, we can write it so: $$(¬A∧¬B)∨(A∧B)$$ because $A\Leftrightarrow B$ is true iff both $A$ and $B$ are true or both $A$ and $B$ are lie.