Using NAND as universal gate

Logisim is the software being used to draw the circuits and display the truth-tables.

NAND gate

Truth table of NAND gate

Implementing NOT gate using NAND

A NAND A = A'

Truth table of A NAND A

OR gate

Truth table of OR gate

Output is 1 when at least 1 input is 1.

Implementing OR using NAND

(A.B)' = A' +B'

A OR B = A + B

We just need to complement the inputs of A and B before feeding them to the NAND gate.

Truth table 

Truth table is same as that of OR gate

AND gate

A NAND B = (A.B)'

A AND B = ((A.B)')'

Just complement the output of NAND

Truth table

Output is 1 only when all inputs are same which is same as AND gate.

Thank you for learning NAND gate as universal gate with me !