Solving Boolean Expression (A' B' C')+(A' B' C)+(A' B C')+(A' B C)+(A B' C')+(A B' C)+(A B C')
Let's look at this function

\$A' + AB'\$

Since the first term is a single input the second term can be implied as...

\$A'\$ or else \$B'\$  

so it is equivalent to 

\$A' + B'\$

This is an absorption law.

So your term 
\$A'+AB'+ABC'\$ can be simplified to
\$A'+ (B'+BC')\$

Then you can do the same with \$B\$ and end up with

\$A'+ B'+ C'\$

Which is btw.

\$(ABC)'\$

ADDITION:

In an attempt to explain the absorption law, let me try to demonstrate it in code.

\$A' + AB'\$ can be expressed as

If Not A then
    Return True
ElseIf A AND Not B Then
    Return True
Else
    Return False
End If


However, the "A" part of the ElseIf is redundant since you would not get there if A were not true, so the code can be simplified to.

If Not A then
    Return True
ElseIf Not B Then &lt;--- A must be true here
    Return True
Else
    Return False
End If


i.e. \$A' + B'\$

The A is implied and true in the second term.