Which of the following arguments are valid? Explain your reasoning a) I have a student in my class who is getting an A. Therefore, John, a student in my class is getting an A
b) Every girl scout who sells at least 50 boxes of cookies will get a prize. Suzy, a girl scout, got a prize. Therefore Suzy sold 50 boxes of cookies.

a) the Statement is Invalid

b) the Statement is Invalid

Explanation:

a)

lets Consider, s: student of my class

A(x): Getting an A

Let b: john

I have a student in my class who is getting ab A: Зs, A(s)

John need not be the student i.e b ≠ s could be true

Hence ¬A(b) could be true and the given statement is invalid

b)

Lets Consider G: girl scout

C: selling 50 boxes of cookies

P: getting prize

s: Suzy

Now every girl scout who sells at least 50 boxes of cookies will get a prize: ∀x ∈ G, C(x) -> P(x)

Suzy, a girl scout, got a prize: s ∈ G, P(s)

since P(s) is true, C(s) need not be true

Main Reason: false → true is also true

Therefore the Statement is Invalid