Need help in representing disjunction in English statement

Suppose I have a predicate, Ex (P(x) ^ Q(x)).

EDIT:

Sorry it was,

Ex (P(x) V Q(x)).


There is atleast one x for which P(x) or Q(x) is true.

Do I have to mention that if both of them are true then also the statement would be true?

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English is slippery. Many people in many contexts (some people in some contexts-logically the same but different feeling) interpret "or" as exclusive or. –  Ross Millikan Nov 5 '11 at 15:42

First, I think the usual notation for disjunction is $\vee$. $\wedge$ usually means "and".

Also, the term "or" as in $A \vee B$ is defined as follows :

A is True, B is True, then $A \vee B$ is True

A is True, B is False, then $A \vee B$ is True

A is False, B is True, then $A \vee B$ is True

A is False, B is False, then $A \vee B$ is False.

Therefore the term "or" (in this context) already includes the case when both are true. So for your expression $(\exists x)(P(x) \vee Q(x))$, it suffices to translation as follows :

There exists an $x$ such that $P(x)$ or $Q(x)$.

In this context, most people will understand the intended meaning of the "or".

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Sorry, I wrote ^ by mistake. It meant OR. Thanks. –  Fahad Uddin Sep 25 '11 at 7:51