11. Logical Operators¶

11.1. and, or, not¶

There are three logical operators: and, or, and not. The semantics (meaning) of these operators is similar to their meaning in English. For example, x > 0 and x < 10 is true only if x is greater than 0 and at the same time, x is less than 10. How would you describe this in words? You would say that x is between 0 and 10, not including the endpoints.

n % 2 == 0 or n % 3 == 0 is true if either of the conditions is true, that is, if the number is divisible by 2 or divisible by 3. In this case, one, or the other, or both of the parts has to be true for the result to be true.

Finally, the not operator negates a boolean expression, so not  x > y is true if x > y is false, that is, if x is less than or equal to y.

11.2. Precedence of Operators¶

We have now added a number of additional operators to those we have learned. It is important to understand how these operators relate to the others with respect to operator precedence. Python will always evaluate the arithmetic operators first (** is highest, then multiplication/division, then addition/subtraction). Next comes the relational operators. Finally, the logical operators are done last. This means that the expression x*5 >= 10 and y-6 <= 20 will be evaluated so as to first perform the arithmetic and then check the relationships. The and will be done last. Although many programmers might place parenthesis around the two relational expressions, it is not necessary.

The following table summarizes the precedence discussed so far from highest to lowest.

11.3. Generic Truth Tables¶

One useful way to think about logical expressions is to use truth tables. A truth table is a table that shows all possible values of a logical expression. Consider the following truth table for the and operator:

The truth table for the or operator is as follows:

The truth table for the not operator is as follows:

For the not operator, there is only one input, so the table is simpler. The not operator simply negates/flips the input.

11.4. Specific Truth Table Example¶

This might be easier to understand if we pick a specific example. Let’s say that p is it is raining and q is it is cold. The truth table would then look like this:

The truth table for the or operator is as follows:

If we combine all of these ideas into a single example, we can see how the truth tables work. Consider the following expression:

not raining and cold or raining

The truth table for this expression would be as follows:

Using a truth table is a useful tool for debugging complex logical expressions. If you are ever unsure about how a complex logical expression will evaluate, you can always write out a truth table to help you understand it.

11.5. Practice Problems¶

11.5.4. Turtle Stuck In a Square¶

You have been given some starter code for the problem below. You only need to change one line of the code, specifically the line containing the while loop. Replace the word something with the appropriate boolean questions that will cause the turtle to continue moving until it gets to one of the edges of the square. Each time the program is run, the turtle will pick a new random direction to move. When executed, your program should look something like this:

Note that you can get the current x coordinate of the turtle by calling bob.xcor(), and the current y coordinate by calling bob.ycor(). Also remember that the turtle begins at the origin (0, 0), which is in the center of the screen. The vertices of the square have x and y coordinates as shown below:

import turtle import random canvas = turtle.Screen() bob = turtle.Turtle() # draw a square to represent the area the turtle needs to stay inside bob.speed(0) bob.penup() bob.goto(-100, -100) # sends bob to a specific coordinate bob.pendown() for side in range(4): bob.forward(200) bob.left(90) bob.penup() # reset turtle to normal starting location bob.goto(0, 0) bob.speed(3) # pick random direction to move some_angle = random.randrange(1, 360) bob.setheading(some_angle) # complete the while statement below # you should only need to adjust one line of code (directly under this comment) while something: bob.forward(5)

11.6. Booleans Practice Quiz¶

To confirm that you understand the boolean variables, you should try the Booleans Practice Quiz using only your brain (in other words, try to figure out what will happen without running the code).