Which of the following is a universal gate?

Definition: A universal gate can be used to implement any logic circuit. NAND and NOR are universal gates.

Using only NAND gates you can implement basic gates as follows: NOT A = NAND(A, A) — connecting both inputs of a NAND to A produces inversion.

AND(A, B) = NAND(NAND(A, B), NAND(A, B)) — a NAND followed by another NAND yields AND.

OR(A, B) = NAND(NAND(A, A), NAND(B, B)) — using De Morgan’s law via NAND-based NOTs gives OR.

Therefore, because NAND alone can produce NOT, AND, and OR, it is a universal gate.