The proposition with double conditionality is referred to as biconditional.
If we look for the term biconditional in the dictionary of the Royal Spanish Academy ( RAE ), we will not find it. The concept, however, is frequently used in the field of philosophy and logic .
A biconditional is a proposition that has a double conditionality , set by the formulas that it relates in a binary way. In colloquial language, the idea is associated with the expression “if and only if” : the biconditional is true if the terms it relates share the truth value (that is, if the two formulas are true or if the two formulas are false ). On the other hand, when the formulas have different truth values (since one is false and the other true), the biconditional is false.
Put another way, a biconditional implies that R is a sufficient and necessary condition for S. It can also be indicated that “if R, then S” and “if S, then R” .
Example of biconditional
Take the example of the following proposition: “A human being biologically belongs to the male gender if he has male reproductive organs.” Leaving aside cultural and identity issues, it can be stated that a human being is part of the male gender “if and only if” they have male reproductive organs.
Returning to the formulas mentioned above: “If a human being biologically belongs to the male gender, then he has male reproductive organs.” This can also be expressed the other way around: “If a human being has male reproductive organs, then he or she biologically belongs to the male gender.” As you can see, we are dealing with a biconditional proposition : it requires that both terms have the same truth value to be true.
In addition to the “particles” or “connections” that we have mentioned that are essential in the biconditional, we cannot ignore other elements that, in the same way, are used in it. We are referring, for example, to “it is necessary and sufficient for” or “it is equivalent to”.
The idea of biconditional is used in areas such as logic, philosophy and mathematics.
The term in mathematics and technology
In the same way, we cannot ignore other really important aspects of the biconditional. We are referring, for example, to the fact that it is also used forcefully within the field of mathematics. In that case, it must be stated that the symbols used to influence the aforementioned biconditional are double-headed arrows , one in each direction.
Likewise, we must keep in mind that, with the advancement of technology, we also come across the fact that it is also important within what is known as digital logic . In this case, the biconditional operator that will be used is XNOR .
More formulas of the biconditional proposition
In addition to what is indicated, in order to summarize certain ideas, we have to start from the fact that the biconditional proposition has several forms of translation, among which we can highlight the following:
-P is a necessary and sufficient condition for q.
-P yes and only yes q. An example would be: “P=A triangle is right angled. Q=A triangle has a right angle”, from which it would emerge that A triangle is a right angle if and only if it has a right angle”.
-If p then q and reciprocally.
-Q is a necessary and sufficient condition for p.
-Q yes and only yes p.
-If q then p and reciprocally.