# “ There exists either a computer scientist or a mathematician who knows both discrete math and C++ ” what will be the logical equivalent sentence?

Assume, $$P(x) : x$$ is a computer scientist. $$M(x): x$$ is a mathematician. $$D(x) : x$$ knows discrete math. $$C(X) : x$$ knows C++.

I translated the sentence into logical statement which is, $$∃x ( ( P(x) ∨ M(x) ) ∧ ( D(x) ∧ C(x) ) )$$ is it correct? and what will be the logically equivalent statement?

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• What's wrong with what you have? – John Douma May 4 at 10:32
• Seems correct. What do you mean by "the logically equivalent statement"? How do you want to transform the statement? For example, you can use the following equivalence: $\exists x S(x)\equiv \neg\forall x \neg S(x)$, for some formula $S$. But there are other transformations, too. – frabala May 4 at 10:40
• The statement is ambiguous. For one, I'd always take either-or to be exclusive, but that may be up to taste. Secondly, should it be "There exists a person who is either a computer scientist or a matician, and this person knwos both discrete math and C++" or perhaps "Either a) there exists a computer scientist who knows both discrete math and C++ or b) there exists a mathematician who knwos both discrete math and C++". Not to mention what could be rewritten as "There exists either a mathematician who knows both discrete math and C++ or a computer scientist" ... – Hagen von Eitzen May 4 at 10:46