Suppose I have a predicate, Ex (P(x) ^ Q(x)).
EDIT:
Sorry it was,
Ex (P(x) V Q(x)).
I made its English statement,
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?
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".