Natural Deduction rules for conjunction

$A\wedge B$ is only true when both $A$ and $B$ are true. Similarly, whenever we know that $A\wedge B$ is true, we know that $A$ and $B$ are both true. This gives us ($\wedge I$) and ($\vee E$) rules as: ?

$$\frac{A,B}{A\wedge B}(\wedge I)\frac{A\wedge B}{A}\text{ and }\frac{A\wedge B}{B}(\wedge E)$$