7.2 Logical Operators

• There are three logical operators: and, or, and not

and

• For example, x > 0 and x < 10is true only if xis greater than 0 and at the same time, x is less than 10

or

• n % 2 == 0 or n % 3 == 0is true if either of the conditions is true

not

• Finally, the notoperator negates a boolean expression, so not  x > yis true if x > yis false

Truth Tables

• To show how logical operators work

a	b	a and b	a or b	not a	not b
T	T	T	T	F	F
T	F	F	T	F	T
F	T	F	T	T	F
F	F	F	F	T	T

Python Quick Note:

• CORRECT:
  • number == 5 or number == 6 or number == 7
• NOT CORRECT:
  • number == 5 or 6 or 7

7.2.1 Logical Opposites

Operator	Definition	Logical Opposites
==	Equals to	!=
!=	Not Equals to	==
<	Less than	>=
<=	Less Than or Equal to	>
>	Greater Than	<=
>=	Greater Than or Equal to	<
- Understanding these logical opposites allows us to sometimes get rid of notoperators
- notoperators are often quite difficult to read in computer code
- Our intentions will usually be clearer if we can eliminate them.

Harder to understand:

if not (age >= 17):
   print("Hey, you're too young to get a driving licence!")

Easier to understand

if age < 17:
   print("Hey, you're too young to get a driving licence!")

De Morgan’s Laws

• Two powerful simplification laws

not (x and y)  ==  (not x) or (not y)
not (x or y)   ==  (not x) and (not y)

Examples

Harder to Understand

if not ((phone_charge >= 0.50) and (phone_storage >= .15)):
   print("You cannot restart your phone. Battery too low or not enough free space.")
else:
   print("Updating now...Several restarts may be required.")

Easier to Understand

if (phone_charge < 0.50) or (phone_storage < .15):
   print("You cannot restart your phone. Battery too low or not enough free space.")
else:
   print("Updating now...Several restarts may be required.")

Easiest Understanding/Implementation

if (phone_charge >= 0.50) and (phone_storage >= .15):
   print("Updating now...Several restarts may be required.")
else:
   print("You cannot restart your phone. Battery too low or not enough free space.")