Lesson 0205: Boolean Expressions¶
Learning Target: I can predict the outcome of boolean expressions.
Right now the programs that we’ve been writing have beem very straightforward  they run instruction after instruction, in the order that it was written. Computers act smart when they can make decisions, and in order to make decisions, we have to learn about boolean expressions.
Simple Boolean Operators¶
A boolean expression is simply any expression that evaluates to be True or False. While we learned about the PEMDAS operators before, none of those apply to boolean expressions. There are three basic operators covered in this lesson:
and
or
not
and
and or
are both operators that require two boolean terms  like True and False
. The not
operator, however, is only applied to a single term.
We can evaluate the expression of boolean expressions with truth tables.
Truth Tables¶
Truth Tables are tables that list all possible outcomes for a given operator. The simplest example of a truth table is the table for the not
operator.
not
¶
The not
operator takes a boolean expression and turns it into its opposite. So if I have True
as my statement, then using not
would turn it into not True
 which is False
.
Here’s how the truth table for not
looks:
If A
is:Then not A
is:True
False
False
True
The way this table is read is as follows:
 if
A
isTrue
, thennot A
isFalse
 if
A
isFalse
, thennot A
isTrue
and
¶
With and
, we require two boolean terms  we’ll call them A
and B
. This time, when we construct our truth table, we will have to list all possible combinations of A
and B
where either one of them can be True
or False
.
If A
is:If B
is:Then A and B
is:True
True
True
True
False
False
False
True
False
False
False
False
I think it’s important to understand the logic behind why this is.
Think of A
and B
being two independent statements that can be either True
or False
. A and B
is a single statement that speaks to the truthiness or falseness of both statements together. As an example, let’s make the following statements:
A
means that the Earth is roundishB
means that the sky is made of lemons
Individually, A
is obviously True
and B
is obviously False
. However, when we think about it in the context of our reallife examples, if you were to say them together as one statement: “The Earth is roundish AND the sky is made of lemons”, then the statement as a whole is false. This is why True and False ==> False
, and False and True ==> False
.
It should be pretty obvious that when you say two truthful statements together, then the entire thing is truthful. Or if you say two false statements together, then the entire thing is false.
As a general rule for and
statements: “A and B” is True as long as both of them are True.
or
¶
With or
, we can logic our way through the truth table. I like making statements for my A
and B
, it makes it easier to understand. Let’s say that:
A
means “it is raining outside”B
means “it is cloudy”
Individually, A
and B
could be True
or False
depending on the weather in your local area. However, if we consider the statement A or B
, meaning “it is raining outside or it is cloudy”, then either one of those statements being True
makes the whole statement True
.
We can still maintain that both being True
is truthful and both being False
is false. Here’s how our truth table looks:
If A
is:If B
is:Then A or B
is:True
True
True
True
False
True
False
True
True
False
False
False
As a general rule for or
statements: “A or B” is True whenever either one of them is True.
Order of Operations & Sample Exercise¶
The order of operations for boolean operators and
, or
, not
are as follows:
 Any parentheses
()
first Then
not
 Then
and
 The
or
last
Make sure you memorize this information! You will need it on the exercises below.
Example: Evaluate the following boolean expression: True and False and not False or True
Step 1: Evaluate all
not
operators:
 True and False and not False or True
 True and False and True or True
Step 2: Evaluate all
and
operators:
 True and False and True or True
 False and True or True
 False and True or True
 False or True
Step 3: Evaluate all
or
operators:
 False or True
 True
Thus our final answer is True
!
Checks for Understanding¶
With booleans, each question really only has one answer  True or False. Therefore, try to make sure you are certain of the answer before you attempt it, otherwise it will be ruined! Try not to guess  guessing will not help you get more comfortable with booleans. Use paper and pencil if you need it  it’s good to show your steps, just like in math class.
Q#1¶
ch02051: Drag the blocks in the order in which they would be evaluated.Parentheses
NOT
AND
OR
Q#2¶

ch02052: Evaluate: True and False or True
 (A) True
 (B) False
 Feel free to check the charts above for reference. Make sure you go step by step!
Q#3¶

ch02053: Evaluate: False or False and not True
 (A) True
 Feel free to check the charts above for reference. Make sure you go step by step!
 (B) False
Q#4¶

ch02054: Evaluate: not (True or True and False and True)
 (A) True
 Feel free to check the charts above for reference. Make sure you go step by step!
 (B) False
Q#5¶

ch02055: Evaluate: True and False and (True and False) or not False or False
 (A) True
 (B) False
 Feel free to check the charts above for reference. Make sure you go step by step!
Q#6¶

ch02056: Evaluate: (False or True) and ((True and False) or not (True or False))
 (A) True
 Feel free to check the charts above for reference. Make sure you go step by step!
 (B) False