Question

The domain of discourse are the students in a class. Define the predicates: S(x): x studied for the test A(x): x received an A on the test What is the logical expression that is equivalent to?

Answer 1

`(\forall x) S(x)\rightarrow A(x)`

`(\exists x)\\eg S(x)\wedge A(x)`

Explanation:

Everyone who studied for the test received an A on the test.

That means- if you studied for the test you will recived an A, and it is hold for everyone, so we will use quantifire
`\forall`.

`(\forall x) S(x)\rightarrow A(x)`

It means: for every student holds- If it is correct that student x studied then the student got an A.

Someone who did not study for the test received an A on the test.

It means that, there is at least one student hwo didn't studie but student got an A. So we have conjuction of two sentences (negation of the S(x) and A(x) for some student- for that we use existential quantifie).

`(\exists x)\\eg S(x)\wedge A(x)`