Propositional Logic - Biconditional

A biconditional is an operator that states that two propositions imply each other. This means that both propositions in a biconditional are necessarily true if one is true, given that the biconditional is true. For a biconditional, we can state the following:

$ v(P↔Q)=T iff v(P)=T and v(Q)=T, or  v(P)=F and v(Q)=F $

Figure 6

Let’s look at the truth table:

P	Q	P↔Q
T	T	T
T	F	F
F	T	F
F	F	T

Table 10

Often times in natural language we say that P if and only if Q, or P is necessary or sufficient for Q, and P is equivalent to Q. Sometimes we say P iff Q. We often use biconditionals in order to state a definition.