Both right? "I don't know anything." and "I don't know nothing." Thanks!
and, I don't know anyone named Tom, or, I don't know nobody named Tom. ?

Question

Both right? "I don't know anything." and "I don't know nothing." Thanks!
and, I don't know anyone named Tom, or, I don't know nobody named Tom. ?

Answer

"I don't know nothing" contains a double negative, which is a no-no in English grammar.

Answer

"I don't know anything" is correct. 
"I don't know nothing" is not correct because good grammar does not contain double negatives.
However, less educated people in the United States might use double negatives, so you might hear them say something like "I don't know nothing."

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