Prove (x+(y (yx))) (yx+yx) = xy

One proof among many possible:

(x+(y (yx))) (yx+yx)
	by simplification 1
(x+(y (yx))) y
	by DeMorgan's Law
(x+(y + yx)) y
	by simplification 2
(x+y) y
	by simplification 3
x y

Some common mistakes:

• x y is not equal to xy
• x yz is not equal to xyz
• xy is not equal to x+ y
• xy = NOT( x+ y)
• Be somewhat careful about how many steps you leave out
  • OK: x to x (y + y)
  • NOT OK: x to x(((y+z)(y+z))+y)
• Some people used the “multiply it all out” approach. That gets cumbersome for bigger proofs.