Propositional Logic - Disjunction

In natural language a disjunction is equivalent to the conjunction ‘or’. This is going to lead us with the following condition:

$ v(P∨Q)=T iff v(P)=T or v(Q)=T $

Figure 3

It should be noted that the rule given by figure 3 is not the way ‘or’ is used in natural language in certain instances. Sometimes ‘or’ is an exclusive or which plays by different rules than the disjunction. For example, when we say that “The dog can be large, or the dog can be small” is only true if either the proposition that “The dog is large” or the proposition that “The dog is small” is true, but not both. For disjunctions, both propositions can be true under the same interpretation. The following is a truth table of a disjunction:

P

Q

P∨Q

T

T

T

T

F

T

F

T

T

F

F

F

Table 5

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