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So, so far we've seen two
ways of creating Booleans.

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We've seen literal expressions
That's either true or false.

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We've seen comparison operators,

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That compare two values.

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So there's equal to, not equal to, less
than, less than or equal to, greater than,

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greater than or equal to.

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And all of these compare one thing on
the left with the one thing on the right.

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And the value of the overall expression
is going to be true or false, again,

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a Boolean.

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Now, there's another way to create
Booleans, which are logical operators.

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So like comparison operators, logical
operators expect one thing on the left and

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one thing on the right.

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So the logical operators that we'll cover,
and, or, and not.

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So and, and or,
just like comparison operators,

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expect one thing on the left,
And one thing on the right.

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Not, only expects one thing that
I'll call B short for Boolean.

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Unlike comparison operators where
the thing on the left and the thing on

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the right can be an integer or string or
pretty much any time logical operators

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expect the thing on the left and the thing
on the right to be Boolean expressions.

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So, the value of L and R is going to
be true if both L and R are true.

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The value of L or R is going to
be true if either L is true or

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R is true, or both are true.

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And, the value of not B is going
to be true only if B is false.

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In order to make it clear how
these logical operators work,

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I'm going to draw what's
called a truth table.

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So, I'll start by drawing
the truth table for, and.

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So, remember that L and
R are both Booleans.

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And, so
L is either going to be true or false.

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So I'm going to represent whether
L is true or false in columns.

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So here, the first column is
going to represent L being true.

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And the second column is going
to represent L being false.

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I'm going to represent
the value of R in rows so

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R being true is the first row and

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R being false is the second row.

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So every cell represents
the combination between L and

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R values represented by that row and
column.

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So here, this cell represents
L is true and R is true.

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This represents L is true and R is false.

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This represents L is false and R is
true and this represents L is false and

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R is false.

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And I'm going to write the value of L and
R in each cell.

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So here if L is true and
R is true then L and R is true.

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If R is false, but L is still true, then
the value of L and R is going to be false.

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And if the reverse were true, so
if L were false but R was true,

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then the value of L and
R is going to be false.

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And if both are false, the value of L and
R is going to be false.

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So you can see that L and R is true
only if L is true and if R is true.

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Let's write out the tree table for or.

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So just like and, we have L and R.

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So we have L true, L false and

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we have R true, R false.

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So if the value of both of these
is true then the value of L or

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R is going to be true.

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If L is true and R is false,
then L or R is true.

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Same thing with if R is true but
L is false.

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The only way that L or R is going to be
false is if L is false and R is false.

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So you can see L or R is going to be
true if either L is true or R is true.

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And then the table for
not is a little simpler.

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So if B is true

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If B is true, then the value
of not B is going to be false.

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If B is false,
the value of not B is going to be true.

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So you can see that not B
is only true if B is false.

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So, when we write out logical operators,

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you don't need to write out
these truth tables entirely.

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But, I use these truth tables as a way
to understand systematically how and,

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or, and not work.

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So, let's look at some code.

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In this code, we assign the variable
x to have the value five, and

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we print up X greater than 0 and
X less than 10.

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So, here on the left,
we have one Boolean expression.

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And, we have another Boolean
expression here on the right.

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What that means is that the value of
this overall Boolean expression is

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going to be true only if this expression
is true and this expression is true.

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So we can check, is x greater than 0?

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Well x is equal to 5 and so
yes 5 is greater than 0.

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So this is true.

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Is x less than 10?

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Well, I see that x is 5 and
yes 5 is less than 10.

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So this is true, and what that
means is that if this is true and

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this is true,
then we're here in our truth table,

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meaning that the value of this
overall expression is true.

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On line four, we assign a variable
n to have the value 25.

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And we print N modulo 2 equals 0.

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Now remember that modulo means remainder,
so

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what this is saying is what's
the remainder of when we divide n by 2.

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So when we pick modulo 2, we're either
going to get 0 if it's an even number,

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or one if it's an odd number because
even numbers will divide by 2 and

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have no remainder.

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Odd numbers will divide by 2 and
have remainder of 1.

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Here we see that n is 25
which is an odd number,

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so n modulo 2 is going to be 1.

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If we take N modulo 3, Matt's asking is
there a remainder when we divide by 3 And

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we should actually have a remainder
of 1 when we divide by 3.

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And so what that means is that
this expression, n modulo 3==0,

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the value of this expression is
going to be false because it's

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comparing 1 with 0 and
checking if they're equal.

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And n%3 == 0.

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The value of this overall expression
is also going to be false

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Because 1 is not equal to 0.

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And so when we ask false or false,
then we fall here in the truth table.

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And false or false is going to be false.

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So I'm printing out true and
then I'm printing out false.

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Let's check our work.

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So you can see we get true,
and then false So if

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you recall from a previous lecture, Python
has a notion of operator precedence.

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So at the highest precedence
Is when we have parentheses.

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And then just below
that is exponentiation.

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That's when we say something like
x**2 which stands for x squared.

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Below that,
we have multiplication and division.

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So that's x times 5 or x divided by 5,

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then we have addition and
subtraction, x plus 2.

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And so our comparison and

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logical operators do fall in
this order of precedence.

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In fact, comparison operators fall just
under addition and subtraction, so

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here we have comparison Like equals equals

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And then below that,
we have the not operator like not x.

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And then below that we have and or

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or so that's like x and y.

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What that means is that if we
have an expression like x greater

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than five and y less than two.

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Then Python is first going to
evaluate this expression because

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this comparison between x and
five has a higher precedence than the and

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And then it's going to evaluate
this overall expression.

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That's all for now until next time