First of all, I have never studied Logic seriously before. I am reading this article on Wikipedia. The definition is the following:
Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.
I would like to know the motivation for this definition. For example, I do not understand why if $A$ is false and $B$ is true, then $ A \wedge B$ is false.