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(a+b'+a'b)c'

=(a+b'+a')c'

=(1+b')c'

=c'
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=[a+(b'+a')(b'+b)]c' distributive law

=[a+(b'+a').1]c' identity 

=[a+a'+b']c' commutative 

=(1+b')c' identity

=c' by theorem x+1=1

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(a+b'+a'b)c'

=(a+a'b+b')c'

=((a+a')(a+b)+b’)c'

=(a+b+b’)c’

=(a+1)c’

=c’

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