Question

Prove algebraically that (x + y)’ . (x’ + y’) = x’ .y^,

Answer 1

LHS = (x + y)’ . (x’ + y’) 

= (x’ . y’) . (x’ . y’) 

= x’ . y’ . x’ + x’ . y’ . y’ 

= x’ . y’ + x’ . y’ 

= x ‘. y’ = RHS 

Hence proved.