Question

Digital logic? Determine whether the following argument's invalid or valid and explain why. A convertible car is fun to drive, Isaac's car is not a convertible, therefore isaac's car is not fun to drive

Answer 1

I said it's invalid b/c it doesn't statethat only convertible cars are fun to drive so therefore we cannot conclude that Isaac's car is not fun to drive. Is there another of explaining this?

Answer 2

Convertible cars belong to the set of cars that are fun to drive. But we don't whether there are other members of this set or what they are.

Isaac's car is not a convertible. But his car could still belong to the set of fun driving cars.

Answer 3

Here's another example along the same lines.

All the mayors of Springfield have been honest men. Mr. Smith is a resident of Springfield but is not or has not been mayor. Therefore he is not an honest man.

This argument is false for exactly the same reasons.

Answer 4

Oh I didn't know this question was about sets.. But it makes sense now. Is there any way to show it with set symbols? If you know what I mean

Answer 5

Sure. Let C be the set of convertible cars and F the set of fun cars. Then
\[C \subset F\]
let x = Isaac's car.
Then\[x \notin C\]
The argument now says
\[x \notin C \implies x \notin F\]
But this is false because we don't that C = F. In other words, there can be cars in F - C and x might be one of them

Answer 6

here's another bad argument:

Practicing Christians belong to the set of people who are not responsible for 9/11. Muslims are not practicing christians therefore they are all responsible for 9/11.

False for the same reasons.

Answer 7

Ohh okay that makes more sense thank you! Just started learning about sets but I get it now