Final answer:
To express the statement using quantifiers, it is \( \forall x, p(x) \) and \( \exists x, \\eg q(x) \), where \( \forall \) indicates 'every' and \( \exists \) indicates 'some' or 'there exists' and \( \\eg \) indicates 'not'.
Step-by-step explanation:
The student is asking about expressing statements using quantifiers. Specifically, they want to express the statement that every student has studied computer programming, but some are not engineers. Using quantifiers, the statement can be written as follows:
\( \forall x, p(x) \) and \( \exists x, \\eg q(x) \)
Where \( \forall \) stands for 'for all' or 'every', \( \exists \) stands for 'there exists' or 'some', and \( \\eg \) stands for 'not'. In this context, p(x) represents that 'x has studied computer programming' and q(x) represents that 'x is an engineer'. So, the statement is saying that for every student x, it is true that x has studied computer programming, and there exists at least one student x for whom it is not true that x is an engineer.
To express the given statements using quantifiers:
i) Every student has studied computer programming, but some are not engineers.
We can use the universal and existential quantifiers to express this statement as:
∀x (p(x)) ∧ ∃x (¬q(x))
This means that for every student x, the student has studied computer programming (p(x)), and there exists a student x who is not an engineer (¬q(x)).