Which of these is a valid conclusion?

Cyclists do not wear fancy hats.
Brenda wears fancy hats.
Therefore Brenda is not a cyclist.

Cyclists do not wear fancy hats.
Brenda is not a cyclist.
Therefore Brenda wears fancy hats.

Cyclists do not wear fancy hats.
Brenda is not a cyclist.
Therefore Brenda does not wear fancy hats.

Cyclists do not wear fancy hats.
Brenda does not wear fancy hats.
Brenda is a cyclist who does not wear a fancy hat.

Question

Which of these is a valid conclusion?

        Cyclists do not wear fancy hats.   
       Brenda wears fancy hats. 
       Therefore Brenda is not a cyclist.
		
Cyclists do not wear fancy hats.   
   Brenda is not a cyclist. 
   Therefore Brenda wears fancy hats.
		
Cyclists do not wear fancy hats.   
   Brenda is not a cyclist. 
   Therefore Brenda does not wear fancy hats.
		
Cyclists do not wear fancy hats.   
   Brenda does not wear fancy hats. 
   Brenda is a cyclist who does not wear a fancy hat.

anonymous · Answer

first one is true

happykiddo · Answer

i'm at crossroads between 1 and 2

happykiddo · Answer

couldnt it be 2

anonymous · Answer

No it can't be two. branda can also be wearing a non fancy hat.

anonymous · Answer

this one?
Cyclists do not wear fancy hats. 
Brenda is not a cyclist. 
Therefore Brenda wears fancy hats.

anonymous · Answer

no not valid

anonymous · Answer

first stament is only about cyclists, says nothing about what happens if you are not a cyclist

anonymous · Answer

It's kinda like saying if you disprove something then you don't prove something else is true from that.

anonymous · Answer

only the first one is valid

anonymous · Answer

It gets confusing.

happykiddo · Answer

so first one ..........are you sure