Question

given: if i drive over the speed limit, then i will get a ticket.
given: i drove over the speed limit.
conclusion: i got a ticket.
answer:

given: if amanda goes to the restaurant, then she will order a hamburger.
given: if she orders a hamburger, then she will get fries.
conclusion: if amanda goes to the restaurant, then she will get fries.
answer:

given: if it snows, then i will wear my snow boots.
given: if it snows, then i will not go to school that day.
conclusion: if i do not go to school, then i will wear my snow boots.
answer:

given: if tina goes to the beach, she will wear sunscreen.
given: tina goes to the beach.
conclusion: tina will wear sunscreen.
answer:

given: if you get a cold, then you eat chicken soup.
given: you ate chicken soup.
conclusion: you must have a cold.
answer:

Explanation:

1. This is an example of the Law of Detachment. If \( p

ightarrow q\) (If I drive over the speed limit, then I will get a ticket) and \( p\) (I drove over the speed limit), then \( q\) (I got a ticket) is valid.

1. This is an example of the Law of Syllogism. If \( p

ightarrow q\) (If Amanda goes to the restaurant, then she will order a hamburger) and \( q
ightarrow r\) (If she orders a hamburger, then she will get fries), then \( p
ightarrow r\) (If Amanda goes to the restaurant, then she will get fries) is valid.

1. The given statements are \( p

ightarrow q\) (If it snows, then I will wear my snow - boots) and \( p
ightarrow r\) (If it snows, then I will not go to school that day). The conclusion \( r
ightarrow q\) (If I do not go to school, then I will wear my snow - boots) is not a valid logical conclusion from the given premises.

1. This is an example of the Law of Detachment. If \( p

ightarrow q\) (If Tina goes to the beach, she will wear sunscreen) and \( p\) (Tina goes to the beach), then \( q\) (Tina will wear sunscreen) is valid.

1. The given statements are \( p

ightarrow q\) (If you get a cold, then you eat chicken soup) and \( q\) (You ate chicken soup). The conclusion \( p\) (You must have a cold) is an example of the fallacy of affirming the consequent and is not a valid logical conclusion.

Answer:

1. Valid (by Law of Detachment)
2. Valid (by Law of Syllogism)
3. Invalid
4. Valid (by Law of Detachment)
5. Invalid