All valid Boolean expressions have a dual, an expression and it’s dual may not be equal but they are both true True or False?

Consensus xy + yz + x’z = xy + x’z Using consensus and other properties simplify to minimum SOP Remember consensus can be used to add a term too XY+X’YZ’+YZ

Simplify to minimum SOP using a Karnaugh map (Sigma the typical symbol for a summation is not available in canvas so we are using S for summation, m means minterm, and d means don’t cares) F(A,B,C,D) = Sm(3,6,7,8,11,12,14,15) + Sd(1,13)

a. z’(x + xy + xyz) =  b. (ab’c)’ac = d. xz + x’yz =  e. ABC’ + AB’C’ + AB’C =  a)    a’bc’ + ab’c’ + a’b’c + a’b’c’ =  b)    (ab + a + abc)c’ =  c)    (x’y + xz + yz)w’ =  d)    (xy)’w + xy =  a)    (a’b’c’)’ =  b)    (ab)’c+abc =  c)    (AB+B+ABC)D = d)   x’ + xy =  e)   A’BC’ + A’B’C’ = 

Find the dual of  ab + ab’ = a

Find the dual of  a+(b+c)

Consensus xy + yz + x’z = xy + x’z Using consensus and other properties simplify to minimum SOP XY+X’YZ’+YZ

Simplify this expression to a minimum SOP (AB’+C’+DE’)(AB’+C’)

Find the dual of  a’b’+a’b+ab+ab’=1

Simplify to minimum SOP A’B’+BC+AC+AB