We can translate this in another way: "Maria being a doctor is a necessary condition for Pedro to be rich" is the same as: "If Pedro is rich, then ...

We can translate this in another way: "Maria being a doctor is a necessary condition for Pedro to be rich" is the same as: "If Pedro is rich, then Maria is a doctor". The knowledge of how to make this translation of the words sufficient and necessary to the conditional proposition format has been demanded enough in contest questions. We cannot forget this: A sufficient condition generates a necessary result. Well then! What will our truth table look like in the case of the conditional proposition? We will think here by exception: this structure will only be false when there is a sufficient condition, but the necessary result is not confirmed. That is, when the first part is true, and the second is false. In all other cases, the conditional will be true. If p and q are represented as sets, through a diagram, the conditional proposition "If p then q" will correspond to the inclusion of set p in set q (p is contained in q): p ⊂ q. About the "... if and only if ..." connective (biconditional): The so-called biconditional structure presents the connective "if and only if", separating the two simple sentences. It is a proposition of easy understanding. If someone says: "Eduardo becomes happy if and only if Mariana smiles". It is the same as making the conjunction between the two conditional propositions: "Eduardo becomes happy only if Mariana smiles and Mariana smiles only if Eduardo becomes happy". Or, said differently: "If Eduardo becomes happy, then Mariana smiles and if Mariana smiles, then Eduardo becomes happy". They are constructions of the same meaning! Knowing that the biconditional is a conjunction between two conditionals, then the biconditional will be false only when the logical values of the two propositions that compose it are different. In short: there will be two situations in which the biconditional will be true: when the antecedent and consequent are both true, or when they are both false. In all other cases, the biconditional will be false. Knowing that the phrase "p if and only if q" is represented by "p↔q", then our truth table will be as follows:

A sufficient condition generates a necessary result.
The conditional proposition will only be false when there is a sufficient condition, but the necessary result is not confirmed.
If p and q are represented as sets, through a diagram, the conditional proposition "If p then q" will correspond to the inclusion of set p in set q (p is contained in q).
The biconditional will be false only when the logical values of the two propositions that compose it are different.