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Exercise 9 (Logical and relational operators)

We advice skimming through or revisiting Exercise 3 ( More on data types and comments).

How are boolean values generated? Logical operators with the use of Relation operators generate Boolean Values. We are saying that when we compare values, boolean values (True or False) are returned as a result.

Relational Operators

Relational operators are binary operators just like the Arithmetic operators. Eg: <, >, <=, >=, ==, != . Hence are sometimes referred to as Comparison operators. They are used for comparing values.

Table of relational operators

Operator Name Use case Return value
< less than 3 < 2 False
> greater than 3 > 2 True
<= less than or equal to 3 <= 2 False
>= greater than or equal to 3 >= 2 True
== equal to 3 == 2 False
!= not equal to 3 != 2 True

Example

# let a and b be two non-zero integers of value 5 and 7 respectively
a = 5
b = 7

# Pay much attention to the Truth values generated

# greater than
print(a > b)
print(b > a)

# less than
print(a < b)
print(b < a)

# greater than or equal to
print(a >= b)
print(b >= a)

# greater than or equal to
print(a <= b)
print(b <= a)

# equal to
print(a == b)
# Not the double equal to. Unlike the assignment operator,
# which is just a character.

# not equal to
print(a != b)
# `!` , means `not`

Logical Operators

Logical operators, combine two or more expressions to generate a boolean value. Eg: and, or, not. This combines more relational expressions to generate a truth value.

The truth tables

The truth table simplifies what truth values are generated when using any of the logical operators.

Assume t as True and f as False

AND table

For an AND table, the truth value becomes True only when both components are True.

a b a and b
t t t
t f f
f t f
f f f

OR table

For an OR table, the truth value becomes False only when both components are False.

a b a or b
t t t
t f t
f t t
f f f

Not table

For a NOT table, when the value is True it becomes False and when it is False then it becomes True. NOT here is the same as negation in some context. If an expression evaluates to True its negation will be False.

a not a
t f
f t

Example

# let a and b be two non-zero integers of value 5 and 7 respectively
a = 5
b = 7

# and
print(a <= 10 and b >= 10)

# or
print(a <= 10 or b >= 10)

# not
print(not a <= 10)
print(not b >= 10)

# compound with logical operators
print((a <= 10) and (b >= 10))

print((a <= 10) or (b >= 10))

print((a <= 10) or (b >= 10))

Note

  • Any value that is None (null - has no value), empty, zero, ... is evaluated to False otherwise True.
  • So all empty structures are evaluated to False by Python.
  • not is unary, then True or not True => True or False => True
  • order of precedence, not, and, or

Practicals

Find the Truth Value of the following:

  • True and not False
  • not True and not False
  • True and False and True or False
  • True or False and True or False

Summary

  • Relational operators are used for comparison
  • Logical operators compound simple relational expressions
  • not is a unary operator