Simplify the Boolean function (x y)+ [ (x+y^ ) y ]^

Step-by-step solution

array rlr & (x y)+ [ (x+y^ ) y ]^ & & =(x y)+ [ (x+y^ )^ +y^ ] & [ (a b)^ =a^ +b^ ] & =(x y)+ [x^ (y^ )^ +y^ ] & [ (a+b)^ =a^ b^ ] & =(x y)+ [x^ y+y^ ] & [ (a^ )^ =a ] & =x y+y^ +x^ y & [ a+b=b+a] & =x y+ (y^ +x^ ) (y^ +y )[ by distributive law ] & =x y+ (y^ +x^ ) 1 & [ a+a^ =1 ] & =x y+x^ +y^ & & =x y+(x y)^ & [ a^ +b^ =(a b)^ ] & =1 & [ a+a^ =1 ] array