3. Boolean logic in Python

In the 19th century, in a book called The Laws of Thought, an Irish mathematician named George Boole developed a formal system of logic that laid the foundation for conveying information electronically. Boolean variables are a special type of variable that has two possible values: True or False. These binary values can also be represented as 1 or 0.

a = True
type(a)

bool

In Python, a double equals sign (==) tests for equivalancy. This is much different from the single equals sign (=), which is used for assignment (assigning a value to a variable).

print(1==1)
print(1==2)

True
False

# 1 and 0 can also represent True or False
print(1==True)
print(1==False)

True
False

# test for non-equivaalence
print(1 != 3)
print(1 >= 3) 

True
False

print(0 == 1)

False

print(0 == False)

True

3.1. Exercise

Predict the output from each of the following three lines of code.

print(True == (0 == 3))

(False == (1 == True)) != False

False = False

3.2. Logic gates

In electronics, logic gates take multiple binary values (on/off) as input and produce a single binary value as output. These logic gates follow the laws of Boolean algebra. The same types of logic gates are used in computer programing. One type of logic gate is the AND gate. The AND gate produces a True value only if both inputs are True.

A logic gate performs a logical operation on multiple binary inputs, resulting in a single binary output.

print(0 and 0)
print(0 and 1)
print(1 and 0)
print(1 and 1)

0
0
0
1

The OR gate produces a True value if at least one input is `True’’.

print(0 or 0)
print(0 or 1)
print(1 or 0)
print(1 or 1)

0
1
1
1

Element-wise boolean logic with Numpy

• Use & for and

• Use | for or

import numpy as np
np.array([True,False,True]) | np.array([True,False,False])

array([ True, False,  True])