Universal gates
-- NAND and NOR gates are called universal gates because all other gates ( AND, OR, NOT, XOR, XNOR) including boolean functions can be realized using these two gates.
1) NAND GATE as a universal gate
1.1) NAND GATE as an inverter (NOT GATE)
1.2) NAND GATE as an AND GATE:
F= X.Y
=> ((X.Y)')'
=> X.Y
1.3) NAND GATE as an OR GATE
F = X+Y
=> ((X+Y)')'
=> (X'.Y')'
F = (X'.Y')'
=> (X')' + (Y')'
=> X+Y