Lecture Notes on Boolean Values and Expressions for CPSC 121 (Fall 2012), Study notes of Computer Science

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• Boolean expressions

Boolean values

What is a Boolean value?

• A value representing either true or false
• After George Boole (logician that invented Boolean logic, circa 1847)

Python has special Boolean values

• True represents true
• False represents false
• Both are of type bool

type(True) <class ’bool’>

type(False) <class ’bool’>

A detail of Python bool values

• bool is a special type of int
• You can think of True as 1 and False as 0

Any non-empty string or list denotes True

bool("spam") True

bool("False") True

bool([20, 10, 30]) True

bool([False]) True

bool("") False

bool([]) False

Boolean expressions

What does a Boolean expression return?

• Boolean values (true or false)

Comparison operators

• The == operator tests if 2 operands are equal (equality)

5 == 5 True

5 == 6 False

True == False False

(5 == 5) == (4 == 4) True

(5 == 5) == (4 == 5) False

The == comparator is one of the (six) relational operators

x != y true if x is not equal to y x > y true if x is strictly greater than y x < y true if x is strictly less than y x >= y true if x ≥ y x <= y true if x ≤ y

Examples

5 != 6 True

6 != (5 + 1) False

2 > 3 False

2 <= 3 True

False < True True # False becomes 0, True becomes 1

[1, 2] <= [1, 2] True

[1, 2, 4] >= [1, 2, 3] True # since 4 >= 3 (subsequences)

Logical operators

And, or, and not form the basic logical operations used in formal logic

• And is often called “conjunction”
• Or is often called “disjunction”
• Not is often called “negation”

The expression x and y is true if x is true and y is true

x y x and y True True True True False False False True False False False False

• This is called a “truth table”

(1 < 2) and (2 < 3) True

1 < 2 and 2 < 3 # parens not needed (but good) True

(1 > 2) and (2 < 3) bool([20, 10, 30]) True >>> bool([False]) True >>> bool("") False >>> bool([]) False ## Boolean expressions What does a Boolean expression return? - Boolean values (true or false) Comparison operators - The == operator tests if 2 operands are equal (equality) >>> 5 == 5 True >>> 5 == 6 False >>> True == False False >>> (5 == 5) == (4 == 4) True >>> (5 == 5) == (4 == 5) False The == comparator is one of the (six) relational operators x != y true if x is not equal to y x > y true if x is strictly greater than y x < y true if x is strictly less than y x >= y true if x ≥ y x <= y true if x ≤ y Examples >>> 5 != 6 True >>> 6 != (5 + 1) False >>> 2 > 3 False >>> 2 <= 3 True >>> False < True True # False becomes 0, True becomes 1 >>> [1, 2] <= [1, 2] True >>> [1, 2, 4] >= [1, 2, 3] True # since 4 >= 3 (subsequences) ## Logical operators And, or, and not form the basic logical operations used in formal logic - And is often called “conjunction” - Or is often called “disjunction” - Not is often called “negation” The expression x and y is true if x is true and y is true x y x and y True True True True False False False True False False False False - This is called a “truth table” >>> (1 < 2) and (2 < 3) True >>> 1 < 2 and 2 < 3 # parens not needed (but good) True >>> (1 > 2) and (2 < 3) False