逻辑运算符

Note

这一节是基于 Jupyter Notebook来生成，你可以点击右上角的Live Code进入编程模式。

布尔运算

乔治.布尔在提出布尔代数的同时，还规定了布尔代数的运算方式，也就是布尔运算（boolean operation)。布尔运算包含三种基本运算符：and，or，not。

and

先来看and运算。这里P和Q都是布尔值。将P、Q的所有组合对应的结果表示出来，如下表所示：

P	Q	P and Q
True	True	True
True	False	False
False	True	False
False	False	False

and运算又称为逻辑与运算：当且仅当P和Q同时为真的时候，P and Q为真；否则P and Q为假。

上表叫做真值表（Truth Table），它列出了所有可能的运算组合。真值表和逻辑运算一一对应。

or

同样，我们可以写出or的真值表：

P	Q	P or Q
True	True	True
True	False	True
False	True	True
False	False	False

or运算又称为逻辑或运算：P和Q至少有一个为真的时候，P or Q为真；否则P or Q为假。

not

not的真值表：

P	not P
True	False
False	True

ex1

a = 10
b = 10
c = -10

if a > 0 and b > 0:
    print("The numbers are greater than 0")

if a > 0 and b > 0 and c > 0:
    print("The numbers are greater than 0")
else:
    print("At least one number is not greater than 0")

#output: "The numbers are greater than 0"
# "At least one number is not greater than 0"

The numbers are greater than 0
At least one number is not greater than 0

ex2

a = 10
b = -10
c = 0

if a > 0 or b > 0:
    print("Either of the number is greater than 0")
else:
    print("No number is greater than 0")

if b > 0 or c > 0:
    print("Either of the number is greater than 0")
else:
    print("No number is greater than 0")


  #output: "Either of the number is greater than 0"
  # "No number is greater than 0"

Either of the number is greater than 0
No number is greater than 0

ex3

x = 50

if not (x>10):
    print("x is no greater than 10")

if not (20 <= x < 40):
    print("x is outside")

x is outside

ex4

def leapYear(year):
    if(year<1582):
        return year%4==0
    else:
        return (year%400==0) or (year%100!=0 and year%4==0)