Type bool

Hi. This lecture is all about true and
false values, also known as Boolean

values. In this lecture, we'll explore the
Python's type bool, and the operators that

we can apply to Boolean values. Earlier,
we used Python's arithmetic operators like

multiplication and subtraction. And now,
we're going to use some of Python's

comparison operators. For example, let's
compare values three and four using the

less than operator. When this expression
is evaluated, we're going to get a true

value or false value back. The type of
value that we get is type bool. Let's

compare three with eight, asking if three
is greater than eight, and it's not. So,

the value that this expression evaluates
to is false. When we evaluate eight

greater than three, we get true. And if we
were to evaluate 3.5 greater than or equal

to 3.4, it's also true. Lets compare two
ends, seven with seven. Notice that the

operation that we're performing now is the
equality operation. And, we need to use

two equal signs, not one, to signify
equality. That's because the single equal

sign is already used for the assignment
operation. Seven is equal to seven. How

about seven and 7.0? I type into operand
with a type float operand. This is also

true. Let's assign a couple of variable
values, x gets seven, y gets eight. And

now, we can apply the same equality
operator to two variable operands. First,

we work up the value that x refers to,
which is seven. And y refers to eight. And

then, seven is compared with eight.
Another operator is the inequality

operator. We can check whether three is
not equal to four, and that's true. The

comparison operators take two values and
return a Boolean value, either true or

false. Python also has three logical
operators, which are operators that are

applied to Boolean values and yield
Boolean results. The first logical

operator that we'll use is the not
operator. And we'll begin by creating a

variable grade and assigning it the value
80. So, grade refers to 80. Now, let's

write up an expression that checks to see
whether the grade i s a passing grade. Is

grade greater than or equal to 50? And
that's true. In Canada, 50 is a pass.

We'll apply the not operator to that
expression now. So, we're going to check

to see whether grade is not greater than
or equal to 50. The order that this

expression is evaluated works from inside
out. So, the grade greater than or equal

to 50 part of the expression is evaluated
first and that gives the value true and

then the not operator is applied to true.
Something that is not true is false. And

that's the result that we get back. We can
apply this not operator two times in a

row, saying that this is asking whether
this is not, not true, which is equivalent

to just saying, is grade greater than or
equal to 50? So, rather than including two

nots in a row, eliminate double negation,
instead write the simpler version of that,

which is to just say, it's great, greater
than or equal to 50. Next, let's use the

and operator. First, we'll make another
variable named grade two. That refers to

the value 70. And now, we'll write an
expression involving both variables grade

and grade two. This expression, we'll
check to see whether both of these are

passing grades. So, is grade greater than
or equal to 50, and is grade two also

greater than or equal to 50? And evaluates
True, if both operands are true. So,

first, this expression is evaluated and it
is true, so then, this expression is

evaluated and it is also true, making this
entire result a true result. Let's change

the value of the variable grade for moment
and set it to 40. We'll rerun this Boolean

expression involving the and, and check to
see what we get. Because this first

operand is false, the Boolean expression
is false. And we don't even go on to check

the second operand's value. Now, let's set
grade back to 80, and this time, change

grade two to be a failing grade. When this
is expression is evaluated, first, this

part of the expression is evaluated. And
that's true so we move on to evaluating

this part of the expression which is
false. And so, the expression ev aluates

to false. To summarize, and again, only
evaluates to true if both of its operands

are true. Otherwise. it evaluates to
false. Finally, lets use the logical

operator or which also applies to two
operands. We'll start by assign grade and

grade two to passing grades. And now,
we'll write the same expression as before

replacing the and with an or. This
expression will evaluate to true if at

least one of the operands is true. So in
this case, we get true. Now, lets assign

to grade a failing grade and reevaluate
the expression. Python will first evaluate

the first part of this expression and
determine that it is false. So, it will go

on to evaluate the second part of the
expression, which is true, and because, at

least one operand is true, the expression
evaluates to true. If we set grade to a

passing grade, and grade two to a failing
grade. Then, when the expression is

evaluated, it works as follows. Because
grade is a passing grade, the, the

expression is evaluated to true at this
point, without even having to go on to

look as the second operand. So, to
summarize, a bool, the Boolean operator or

evaluates to true if at least one of its
operands is true. And it evaluates to

false otherwise. Now, let's combine the
operators into single expressions. I've

assigned grade and grade two passing
grades of 80 and 90, and I'd like to

evaluate this expression. I'm going to
apply not to grade greater than or equal

to 50, or grade two greater than or equal
to 50. And there are a couple of different

ways that we can interpret this
expression, depending on order of

precedence. The first would be to have the
or operator applied first, and I'll use

parentheses to signal that, followed by
the not operator. The second would be to

actually have the not operator apply first
to the first part of the expression. And

then, the or operator apply second. So,
not first, followed by or, or, or first

followed by not. Let's evaluate the
expression and see what happens. [typing

sound] The value that the expression
evaluates to is true. An d let's use the

parentheses to see which of the two
operators applied first. We'll begin by

putting the parentheses around the or part
of the expression, ensuring that or

applies before not. And when we do that,
the result is false. So, that's not what

happened when we left off the parentheses,
parentheses. And that means that that's

not the order of precedence. Instead, the
order of precedence is that not is applied

first, as I can show here, followed by or.
The order of precedence for logical

operators is not, and, and then or. And
when we're working with multiple logical

operators within an expression, we can use
parentheses to ensure that the operations

apply in the order we'd like without
having to worry about what the order of

precedence is. Sometimes, we'll use
parentheses to make an expression more

readable. For example, in this expression,
the arithmetic operators have higher

precedence than the Boolean operators or
logical operators, so these parentheses

are unnecessary but we include them for
readability. Instead, we could have left

off the parentheses and had the following,
where some, I find a little harder to read

and understand.