What are Mathematical Statements? Video Lecture | Applied Mathematics for Class 11 - Commerce

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what does a statement a statement is
something that gives us information for
example Jerry is smarter than Tom now
this is considered to be a statement in
the English language but can we say that
this is a mathematical statement no
let's understand why that is because for
some people Jerry may be smarter than
Tom but for others that may not be the
case so this is an ambiguous statement
it's neither true nor false such
statements are not acceptable in
mathematics hence this is not a
mathematical statement so what is a
mathematical statement a statement is
called a mathematically acceptable
statement if it's either true or false
but not both now consider this example
tom is taller than Jerry can you tell me
whether this is a mathematical statement
or not yes this is a mathematical
statement why do I say so as the heights
of Tom and Jerry can be measured we can
always verify the statement it will
either be true or false so this is a
mathematical statement now let's look at
a few more statements here's the first
one
what a beautiful day is this a
mathematical statement it's not because
an exclamation can never be a
mathematical statement so the statements
like wow and the food was amazing are
also not mathematical statements here's
another one sit straight
mathematical statement or not notice
that this is an order and an order can
never be a mathematical statement so
statements like open the door and raise
your hand are also not mathematical
statements ok next all squares are
rectangles what do you think
yes it's a mathematical statement
because we can definitely say that it's
true
next what is your name this is a
question and a question can never be a
mathematical statement what about these
two statements here she could mean any
girl and here could be any place she and
here are pronouns and statements
involving pronouns cannot be considered
as mathematical statements are you ready
to try out a few more examples okay here
we go
consider this statement the sides of all
the quadrilaterals are equal is this a
mathematical statement yes it is because
we definitely know that it's a false
statement remember it could either be
true or false it doesn't only have to be
true okay now for the final two examples
here they are
is this one a mathematical statement we
should note that statements involving
variable time such as today tomorrow or
yesterday are not considered to be
mathematical statements why this example
for instance will be true only on
Wednesday and not on any other day so it
may be true or false what about the
second one
correct it's not a statement that's
because geometry may be interesting for
some but not for others it means that
this statement is true for some and
false for the others hence this does not
qualify as a mathematical statement let
me leave you with an interesting quiz
can you tell me whether the two
statements given below our mathematical
statements or not one sum of two
integers is positive to sum of two
integers can never be negative
tell us your answers below also how our
mathematical statements represented and
what is the negation of a statement
let's see that in the next part
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you