Either, neither, both

The words either, neither, and both are all used to talk about how two objects
relate to each other. “Either” means “X OR Y” (but not both):

“Was either of the drivers hurt in the accident?”
“Either John OR Carol can do the job.”

“Neither” means “NOT X and NOT (NOR) Y.” Although people often use “or” with
“neither,” it is more grammatically correct to use “nor”:

“Neither Frank nor John came to the party.”
“Neither of the music stores has the CD.”

“Both” means “X and Y”:

“I've got holes in both of my shoes!”
“Both the front tire and the back tire are flat.”