Simplying Boolean-Logic Expression

Question

Can you help me simplify this or is this the simplified form?

A = (X + Y + Z) (X + ~Y + ~Z) (~X + Y + ~Z) (~X + ~Y + Z)

Here's my attempt:

 A = (X + Y + Z) (X + ~Y + ~Z) (~X + Y + ~Z) (~X + ~Y + Z)

Using De Morgan's Law:
     ~ [A = (X + Y + Z) (X + ~Y + ~Z) (~X + Y + ~Z) (~X + ~Y + Z)]

     ~A = ~[(X + Y + Z) (X + ~Y + ~Z) (~X + Y + ~Z) (~X + ~Y + Z)]

     ~A = (~X ~Y ~Z) + (~X Y Z) + (X ~Y Z) + (X Y ~Z)

     ~A = ~X (Y XNOR Z) + X (Y XOR Z)
          Let v = (Y XOR Z)
          ~A = ~X ~v + X v
          ~A = X XNOR v
          Subtituting v: ~A = X XNOR Y XOR Z

     ~A = X XNOR Y XOR Z

Applying De Morgan's Law again:
     ~A = X XNOR Y XOR Z

     ~ [~A = X XNOR Y XOR Z]

     A = ~(X XNOR Y XOR Z)

Now I'm stuck at that step. I don't know if I should still apply the NOT or NEGATE or leave it as that.

If I apply it, is this the right answer?

A = ~X XNOR ~Y XOR ~Z

Answer 1

The original expression and your final answer both result in the same minterms:

XYZ or ~X~YZ or ~XY~Z or X~Y~Z

             XY
       00  01  11  10
      +---+---+---+---+
   0  | 0 | 1 | 0 | 1 |
Z     +---+---+---+---+
   1  | 1 | 0 | 1 | 0 |
      +---+---+---+---+