This is to help you practice simplifying logic expressions quickly. Simplify the following expressions, where x is an arbitrary proposition variable (has value 0 or 1). Legend:

+ is or

· and juxtaposition are and

´ is not

is implies

is iff (if and only if)

x + 0 =

x + 1 =

x · 0 =

x · 1 =

x 0 =

x 1 =

0 x =

1 x =

x 0 =

x 1 =

0 x =

1 x =

x + x´ =

x · x´ =

x x´ =

x x´ =

x + x´ y =

x´ + x y =

(x´ + y´)´ =

(x´ · y´)´ =