The truth table lists all the possible combinations of the truth values of the starting propositions and, for each, the value of the connective. With two propositions and there are four cases to examine.
Property — Truth table of the connectives
p & q & \lnot p & p\land q & p\lor q & p\Rightarrow q & p\Leftrightarrow q \\ \hline V & V & F & V & V & V & V \\ V & F & F & F & V & F & F \\ F & V & V & F & V & V & F \\ F & F & V & F & F & V & V \end{array}$$
We observe the essential rules: the conjunction is true only when both are; the disjunction is false only when both are; the double implication is true when and have the same truth value.
Links
Topics: Set theory
Concepts: Logical connectives · Truth table
Skills: Reasoning by cases