Question

 A multiplexer (MUX) is a logic function that combines several inputs and a control input, the output of which is one of the inputs selected by the control input. A2-1 MUX is shown below:

 Where X and Y are inputs and S is the control input. The Truth Table of the 2-1 MUX is given by:

 Show that the 2-1 MUX forms a complete set of logic functions by realizing a NOR gate using only 2-1 MUXes.

Answer 1

There are two possible designs by which we can prove the statements:

Option01:

Here if A == 0; then OUT = (NOT) B.

else if A == 1; then OUT = 0

Option 01
Inputs		Output
X	Y	OUT
0	0	1
0	1	0
1	0	0
1	1	0

Option 02:

Here if B == 0; then OUT = (NOT) A.

else if B == 1; then OUT = 0

Option 02
Inputs		Output
X	Y	OUT
0	0	1
0	1	0
1	0	0
1	1	0

Hense we can say that, both of the options forms complete set of logical function.