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5.5. DeMorgan’s Laws¶
DeMorgan’s laws were developed by Augustus De Morgan in the 1800s. They show how to handle the negation of a complex conditional, which is a conditional statement with more than one condition joined by an and (&&) or or (||), such as
(x < 3) && (y > 2).
not (a and b) is the same as (not a) or (not b). In Java this is written as !(a && b) == !a || !b
not (a or b) is the same as (not a) and (not b). In Java this is written as !(a || b) == !a && !b
Applying DeMorgan’s Laws to
!(x < 3 && y > 2) yields
!(x < 3) || !(y > 2) which means that this complex conditional will be true when
(x >= 3 || y <= 2).
Notice that the negation is distributed to all parts of a complex conditional. It negates each part of the conditional and changes and (&&) to or (||) and or (||) to and (&&).
The negation modifies each conditional as shown below.
< becomes >=
> becomes <=
== becomes !=
<= becomes >
>= becomes <
!= becomes ==
See the example below. For what values of x and y will it print true? Try out different values of x and y to check your answer.
For more information about DeMorgan’s laws see http://en.wikipedia.org/wiki/De_Morgan’s_laws.