A NAND B is equivalent to
NOT (A
AND B)
A
NOR B is equivalent to
NOT (A
OR B)
A
XNOR B is equivalent to (
you guessed it)
NOT (A
XOR B)
There are also a few others: implication and biconditional.
Implication is false iff A is true and B is false. It is equivalent to (NOT A) OR B. It can also be written "If A then B".
Biconditional is true iff A and B have the same truth value. In fact, iff is biconditional. It is equivalent to A XNOR B or (A implies B) AND (B implies A).