Predicate Logic expressions

Question

Consider the following predicates:

• English (x): x speaks English

• Mathematics (x): x knows math

• Computer (x): x is a computer science student

(a) There is some computer science student who does not know mathematics or speaks English

(b) Every computer science student knows mathematics but does not speak English

1) Domain: set of all the students of Computer Science

(a) $∃x(¬Mathematics(x)∨English(x))$

(b) $∀x(Mathematics(x)∧¬English(x))$

2) Domain: set of all students

(a) $∃x[Computer(x)∧(¬Mathematics(x)∨English(x))]$

(b) $∀x[Computer(x)→(Mathematics(x)∧¬English(x))]$

Can you please tell me if these 4 logic expressions are correct? Thanks.

Answer 1

Yes, they are correct.   You have the right connectives and quantifiers in place.

Answer 2

I would say that:

(a) There is some computer science student who does not know mathematics or speaks English

is ambiguous. My initial reading of this was that this student does not know mathematics and that this student also does not speak English, i.e. I read it as a negation of a disjunction, in which case you would get:

1a. $\exists x \ \neg(Mathematics(x) \lor English(x))$

2a. $\exists x \ [Computer(x) \land \neg(Mathematics(x) \lor English(x))]$

But of course your reading makes sense as well ... maybe you can get some clarification what was meant? Otherwise, you may want to say that the sentence is ambiguous and provide symbolizations for both interpretations.