### De Morgan's Laws

Posted:

**21 Feb 2013, 22:20**Simplify Boolean expressions using the De Morgan's Laws :

(NOT P) OR (NOT Q) can be expressed shorter as NOT (P AND Q)

(NOT P) AND (NOT Q) can be expressed shorter as NOT (P OR Q)

So, in that situation, use the NOT operator only once, as shown below.

EXAMPLE 1 - "AND" BECOMES "OR"

The expression

PB:

Java:

should be simplified to

PB:

Java:

EXAMPLE 2 - "OR" BECOMES "AND"

(To go to a restaurant, 2 conditions must be satisfied: "we are hungry" AND "restaurants are open now"):

The expression

PB:

Java:

should be simplified to

PB:

Java:

(NOT P) OR (NOT Q) can be expressed shorter as NOT (P AND Q)

(NOT P) AND (NOT Q) can be expressed shorter as NOT (P OR Q)

So, in that situation, use the NOT operator only once, as shown below.

EXAMPLE 1 - "AND" BECOMES "OR"

The expression

PB:

- Code: Select all
`lb_is_gas = (not lb_is_liquid) and (not lb_is_solid) and (not lb_is_plasma)`

Java:

- Code: Select all
`isGas = (!isLiquid) && (!isSolid) && (!isPlasma);`

should be simplified to

PB:

- Code: Select all
`lb_is_gas = not (lb_is_liquid or lb_is_solid or lb_is_plasma)`

Java:

- Code: Select all
`isGas = !(isLiquid || isSolid || isPlasma);`

EXAMPLE 2 - "OR" BECOMES "AND"

(To go to a restaurant, 2 conditions must be satisfied: "we are hungry" AND "restaurants are open now"):

The expression

PB:

- Code: Select all
`lb_we_will_stay_home = (not lb_we_are_hungry) or (not lb_restaurants_are_open_now)`

Java:

- Code: Select all
`weWillStayHome = (!weAreHungry) || (!restaurantsAreOpenNow);`

should be simplified to

PB:

- Code: Select all
`lb_we_will_stay_home = not (lb_we_are_hungry and lb_restaurants_are_open_now)`

Java:

- Code: Select all
`weWillStayHome = !(weAreHungry && restaurantsAreOpenNow);`