Logical Connectives.

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I have a statement.

Every student at your school either can speak Russian or knows C++.

Where P(x) is the statement "x can speak Russian". And Q(x) is the statement is the statement "x knows the computer language C++". I have to express this in terms of logical connectives. Here's what I did.

∀x(P(x) ∨ Q(x))

Is this correct?

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Basicly, if either also include both, your answer is correct.

If not, you will need to write $$\forall x,(P(x)\land\neg Q(x))\lor (\neg P(x)\land Q(x))$$

In general, one of $p,q$ is true but not both can be written as $p⊕q$, and have following equivalent forms:

$$p⊕q\equiv (p\land\neg q)\lor (\neg p\land q)\equiv(p\lor q)\land(\neg p\lor\neg q)\tag*{aka Xor}$$

Sometime it's hard to tell if it means both or not, you can also check this post.