Question

write the negation of the statement:
No vans have three wheels

Answer 1

There exists a van that has 3 wheels.

Answer 2

All vans have three wheels.

Answer 3

Ok, so if I had one that said No bicycles have three wheels ... since this is a true statement the negation would be some bicycles have three wheels?

Or would it be some bucycles do not have three wheels?

Answer 4

@ash2326 you don't negate a statement with universal quantifier using another universal quantifier. If you were to tell me "All dogs have 16 legs," to negate that, all I have to reply is "No, I know there exists one dog that doesn't have 16 legs."

Answer 5

If you told me, "No bicycles have three wheels," that's the same as saying "There does not exist a bicycle that has three wheels." Does that make sense?
In order to negate that statement, you don't need to say, "All bicycles have three wheels." It's enough to just say that there is one bicycle with three wheels to negate it.

Answer 6

Already had this book out in front of me, studying for the same class, I assume. We did that stuff about a month ago and it's the only thing I actually understand, haha

Answer 7

LOL well thank you and because of your explanation I understand now!! Good luck to you!!

Answer 8

Thanks, you too. If you have any more questions, feel free to message me.