Here is a problem from Kenneth Rosen's Discrete Mathematics and its Applications, Section 1.4
Let P (x) be the statement “x can speak Russian” and let Q(x) be the statement “x knows the computer language C++.” Express each of these sentences in terms of P (x), Q(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school. This is a homework problem and I am not expecting a complete answer.
Every student at your school either can speak Russian or knows C++.
The answer to this problem was ∀x(P(x) V Q(x))
But I think it should be ∀x(P(x) ⊕ Q(x)) by the exclusive or XOR not inclusive or as the statement is either or
where is the correct answer? and why?