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top: (X+X') at X = 1
lower: (X+X') at X = 0
As you can see the two simulations above produce equal results even
though they are both implimented differently. This is due to the fact that
whenever you have a variable and it's complement OR'ed it will always produce
one... if either one is zero its complement is one and so the statement
is true. If either one is "1" then it automatically makes the statement
true!
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Let us demostrate via a simulation:
First [X+YZ]:
Second [(X+Y)(X+Z)]:
As you can see in the above images... again the implimentation from
the previous diagram is different but it still complies with the truth
table.