How is it possible to deduce $A$ from $A\wedge B$? If I know that $A\wedge B = T$  then I can say that surely $A$ and $B$ separately are true, but if $A\wedge B = F$ then how can I infer the truth value of $A$ or the one of $B$. It seems impossible to infer the result : I can say just that  $¬A∨¬B = T$. What am I missing? Am i misuderstanding the process of making deductions?

EDIT:

Is it linked to the fact that $A\wedge B\implies A$ is a tautology? Because this is the reason given in my book. Should I consider just the case $A\wedge B = T$ ?
Looking at the truth-table is helpful for $A \wedge B$
$$
\begin{matrix}
A &amp; B &amp; A \wedge B \\ \hline
F &amp; F &amp; F \\
F &amp; T &amp; F \\
T &amp; F &amp; F \\
T &amp; T &amp; T 
\end{matrix}
$$
If you know that $A \wedge B=F$, it could be any of the first three cases.  So you cannot infer $A$'s state or $B$'s state, but you can infer that one of them is false.
If (A $\land$ B) is false, then inferring either A or B is not valid.  In general, inferring anything from a false premise is not valid, though there do exist exceptions such as if (A &lt;-&gt; B) is false, and B is false, then A is true.
Often enough though, in formal systems, it's required that a formula holds true for inferences to get made from it (and the rule of inferences used always preserve truth also).  That's one reason why the axiomatic method has something to recommend to it, and sometimes gets regarded as more rigorous.