What's FORMAL Logic Notation? Logic Inference Problem too

Question

Is this a proper example of FORMAL logic notation? (Ǝ c ∈ Cookies such that Ǝ d ∈ duck, d wants c)

I have a question that requires an answer in 'formal' logic notation. I'm assuming that they're making a distinction between 'normal' logic notation as in: p ^ q -> r

Question 2: I have a question that reads:

Use truth table to determine whether the following arguments are valid or not. If (~p ∨ q ∨ r) holds and (q->r) holds, then infer that (p->r) holds. Here (~p ∨ q ∨ r) and (q ∨ r) are premises; (p->r) is the conclusion.

I'm not sure if the question is asking if (~p ∨ q ∨ r) ^ (q ∨ r) = (q->r) If that's the case then the arguments are false. At lease in the case of p=F, q=T, r=F. Am I on the right path?

EDIT: 'COMMENT'

So the question is basically: Given: (~p ∨ q ∨ r) ^ (q ∨ r) = (q->r) is this true?

Answer 1

For 1., the "formal" notation, using predicate logic, will be :

$(Ǝ c ∈ Cookies)(Ǝ d ∈ Ducks)Wants(d,c)$.

For 2., you have to show that :

$(\lnot p ∨ q ∨ r) \land (q ∨ r) \vDash (q \to r)$,

i.e. the conjunction of the premises logically implies the conclusion. It does not means necessarily that premises and conlcusion are logically equivalent : in this case, as you noticed, they are not.