6.7. Truth Tables

Truth tables help us understand how logical operators work by showing all of the possible return values. Let’s look at the truth table for and, which assumes we have two boolean expressions, A and B.

6.7.1. Truth Table for and

Example

A B A and B
True True True
True False False
False True False
False False False

Consider the first row of the table. This row states that if A is true and B is true, then A and B is true. The two middle rows show that if either A or B is false, then A and B is false. Finally, if both A and B are false, then A and B is false.

6.7.2. Truth Table for or

Example

A B A or B
True True True
True False True
False True True
False False False

Similar to the and table, if A or B are both true, then A or B is true. However, the middle two rows show that if either A or B is false, then A or B still remains true. This is very different from the and table. The last row shows that if both options are false, then the entire statement is false.

6.7.3. Order of Operations

We now have a lot of operators in our toolkit, so it is important to understand how they relate to each other. Which operators get done first?

Python always performs operations in a specific order:

  1. It does all math calculations first.
  2. Next, it evaluates all comparisons as True or False.
  3. Next, it applies all not operators.
  4. Finally, it evaluates and and or operations.

Example

The expression x * 5 >= 10 and y - 6 <= 20 will be completed in this order:

  1. x * 5 is calculated, then y - 6.
  2. The >= comparison is evaluated as True or False.
  3. The <= comparison is evaluated as True or False.
  4. The and operator is evaluated last.

Let’s say x = 2 and y = 46. Here we step through each stage of the evaluation:

Operator Order on: x * 5 >= 10 and y - 6 <= 20
Action Result
Plug in the values into the expression 2 * 5 >= 10 and 46 - 6 <= 20
x * 5 is calculated, then y - 6 10 >= 10 and 40 <= 20
The >= comparison is evaluated as True or False True and 40 <= 20
The <= comparison is evaluated as True or False True and False
The and operator is evaluated last False

6.7.3.1. Table of Operator Order

The following table lists operators in order of importance, from highest (applied first) to lowest (applied last).

Operator Order
Level Category Operators
(Highest) Parentheses ()
  Exponent ** (For example: 2**3)
  Multiplication and Division *  /  //  %
  Addition and subtraction +  -
  Comparison ==  !=  <=  >=  >  <
  Logical not
  Logical and
(Lowest) Logical or

Tip

Using parentheses is not always necessary, but they make a BIG difference when someone else reads your code. As a best practice, use parentheses to make your code easier to read:

x * 5 >= 10 and y - 6 <= 20

vs.

(x * 5 >= 10) and (y - 6 <= 20)

6.7.4. Check Your Understanding

Question

Assume we have 3 boolean expressions (A, B, and C). Which combinations of values (A/B/C) will make the expression A or B and C evaluate to True?

  1. True / True / True
  2. False / True / True
  3. True / False / True
  4. True / True / False
  5. False / False / True
  6. False / True / False
  7. True / False / False
  8. False / False / False