Simplify Boolean Expression: X + X'Y'Z

Question

I know that the following is equal: X + X'Y'Z = X + Y'Z How can simplify the left side to arrive the right side using basic Boolean identities? Thanks in advance.

Just think about under which circumstance the right term is needed to get a `true` result, and which value X then must have. — Rudi, Feb 18 '20 at 06:35

score 1 · Accepted Answer · answered Feb 19 '20 at 14:05

Expression                            Justification
---------------------------------     -------------------------
X + X'Y'Z                             initial expression
(XY'Z + X(Y'Z)') + X'Y'Z              r  = rs + rs'
(XY'Z + XY'Z + X(Y'Z)') + X'Y'Z       r = r + r
(XY'Z + X(Y'Z)' + XY'Z) + X'Y'Z       r + s = s + r
(XY'Z + X(Y'Z)') + (XY'Z + X'Y'Z)     (r + s) + t = r + (s + t)
X(Y'Z + (Y'Z)') + (Y'Z)(X + X')       rs + rt = r(s + t)
X(1) + (Y'Z)(1)                       r + r' = 1
X + Y'Z                               r(1) = r

Thank you, your solution/answer and the reference to the YouTube demo was helpful. — Russell, Feb 19 '20 at 15:48

score 0 · Answer 2 · answered Feb 21 '20 at 22:53

0

The fastest way to prove this expression is to add a redundant term that will discard X'

X + X'Y'Z = X(1+Y'Z) + X'Y'Z
          = X + XY'Z + X'Y'Z
          = X + (X+X')Y'Z
          = X + Y'Z

answered Feb 21 '20 at 22:53

Alain Merigot

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Simplify Boolean Expression: X + X'Y'Z

2 Answers2