VALIDITY OF AN ARGUMENT (MATH IN THE MODERN WORLD) - Tagalog Tutorial
Summary
TLDRThis video lesson focuses on evaluating the validity of logical arguments using truth tables. The instructor explains how to determine if an argument's conclusion is valid by examining the truth values of premises. Examples are provided, including arguments with 'if P then Q' and their negations. The lesson clarifies that a valid argument is one where the conclusion is always true when the premises are true, using the concept of tautology. The video also includes practice exercises for viewers to test their understanding of argument validity.
Takeaways
- 📘 The video discusses the validity of an argument in symbolic form.
- 🔍 It focuses on determining whether a given argument's conclusion is valid or invalid.
- ✍️ Example 1 uses the symbolic form: 'If P then Q and P, therefore Q', which is analyzed for validity.
- ✅ Truth tables are used to evaluate if the premises and conclusions hold true or false.
- 🔗 In this case, when both premises are true, the conclusion is also true, confirming the argument is valid.
- ⚠️ Example 2 is another argument: 'If P then Q and Q, therefore P', which is found to be invalid.
- 🔄 The video continues with different examples to test various logical structures using truth tables.
- 📉 Example 3, involving 'If R then S and not S, therefore R', is analyzed and found to be invalid.
- ❌ The final example also involves negation ('If M then not K and not M, therefore K'), which is evaluated as invalid.
- 📝 The video ends with a practice exercise for viewers to test the validity of an argument, encouraging engagement through comments.
Q & A
What is the main topic discussed in the video?
-The main topic discussed in the video is the validity of an argument in logic, with a focus on determining whether the conclusion of an argument is valid or invalid using truth tables.
What is the symbolic form of the first argument example provided?
-The symbolic form of the first argument is: If P then Q, and P, therefore Q.
How is the validity of the first argument determined?
-The validity of the first argument is determined using a truth table. If both premises are true, then the conclusion must be true, making the argument valid.
What is the conclusion of the first argument example?
-The conclusion of the first argument example is that the argument is valid.
What is the structure of the second argument discussed?
-The structure of the second argument is: If P then Q, and Q, therefore P.
Is the second argument valid or invalid, and why?
-The second argument is invalid because the truth table does not result in a tautology, meaning the conclusion is not necessarily true.
What is the symbolic form of the third argument example?
-The symbolic form of the third argument is: If R then S, and not S, therefore not R.
Why is the third argument considered invalid?
-The third argument is considered invalid because the truth table does not produce consistent true outcomes across all interpretations, meaning the conclusion is not guaranteed.
How is the fourth argument structured in symbolic form?
-The fourth argument is structured as: If M then not K, and not M, therefore K.
What is the conclusion for the fourth argument example?
-The conclusion for the fourth argument example is that the argument is invalid, based on the truth table analysis.
Outlines
📊 Understanding Argument Validity in Symbolic Logic
In this section, the speaker introduces the lesson on argument validity in symbolic form, continuing from the previous video. They explain the focus will be on determining if conclusions of arguments are valid or invalid. The first example, 'If P, then Q' and 'P, therefore Q', is discussed using truth tables. The explanation shows how to determine whether the conclusion is valid by checking different truth values for P and Q, ultimately concluding that the argument is valid based on truth table analysis.
🧠 Validity of Arguments Through Truth Tables
This paragraph continues the discussion on argument validity. The speaker further elaborates on truth tables, testing combinations of truth values for premises and conclusions. They explain tautology, which is a statement true under all interpretations. For this argument, 'If P, then Q' and 'P, therefore Q' is again shown to be a valid argument. A second example is introduced, where 'If P, then Q' and 'Q, therefore P' is examined, and the truth table is set up to determine the argument's validity.
❌ Analyzing an Invalid Argument
The speaker analyzes a second example using the symbolic form 'If P, then Q' and 'Q, therefore P.' The truth table shows different truth values for P and Q. After thorough analysis, the speaker concludes that the argument is invalid because it does not meet the criteria for tautology. The explanation highlights how the premises and conclusion fail to align consistently, leading to the argument being considered invalid.
🌀 Exploring Another Invalid Argument
In this example, the speaker introduces an argument in symbolic form: 'If R, then S' and 'Not S, therefore R.' The argument is analyzed using truth tables with specific emphasis on the negation of S. The speaker demonstrates how negations work in truth tables and how the given premises and conclusion interact. The analysis leads to the conclusion that this argument is also invalid, with explanations rooted in the lack of tautology.
🔄 Determining Validity in Complex Arguments
Here, the speaker presents a new argument in symbolic form: 'If M, then not K' and 'Not M, therefore K.' Truth tables are used to explore different truth values for M and K. The speaker carefully explains how to apply conjunctions and negations in the truth table analysis. Ultimately, the conclusion is that this argument is invalid. The speaker ends by encouraging viewers to practice determining the validity of arguments and leave their thoughts in the comments.
Mindmap
Keywords
💡Validity
💡Truth Table
💡Premises
💡Conclusion
💡If-Then Statement
💡Tautology
💡Invalid Argument
💡Negation
💡Conjunction
💡Symbolic Logic
Highlights
Introduction to argument validity and determining if an argument is valid or invalid.
Explanation of the symbolic form of arguments and using truth tables to verify validity.
Example 1: If P then Q and P, therefore Q—valid argument based on truth table results.
Explanation of truth table for 'if-then' statements with combinations of true and false premises.
Clarification that if both premises in an 'if-then' statement are false, the result is still true.
Detailed walk-through of evaluating symbolic logic and the conjunction of propositions.
Example 2: If P then Q and Q, therefore P—determined to be an invalid argument based on truth table results.
Introduction to the concept of tautology—a statement that is true under any interpretation.
Example 3: If R then S, and not S, therefore R—an invalid argument as demonstrated by the truth table.
Explanation of negation and its role in the evaluation of logical propositions.
Example 4: If M then not K, and not M, therefore K—invalid argument as shown through the truth table.
Use of conjunction and negation in complex logical evaluations.
Step-by-step guide to constructing and interpreting truth tables for various symbolic arguments.
Conclusion on the importance of truth tables in verifying the validity of arguments.
Practice exercise provided to allow viewers to determine the validity of an argument using truth tables.
Transcripts
foreign
good day everyone Welcome to our new
video Lesson in mathematics and the
modern world for this video we will
discuss the validity of an argument
last video
in our last video Lesson we've discussed
about the argument in symbolic form so
for this video we will have the
conclusion we will determine if the
conclusion of an argument is valid or
invalid
okay so arguments validity so example
number one you have our argument so if P
then q and P therefore Q so in symbolic
form that will be written as if P then q
and P therefore Q
so we will just determine if the given
argument is valid or invalid
okay
Boys
in our if then through table so if both
are true if both of the premises are
true so the conclusion is true then if p
is through p is false the conclusion is
false then if p is false Q is true the
conclusion is true if both are false so
that is true so um
automatically the if then is false and
then that is
and second truth tables
p and Q
sorry
letter f
in one of the
proposition automatically
an acting conjunction is f or false
both propositions are true
I think
argument if the argument is valid or not
so um
if P then q and P then you have the
argument if P then q and P therefore Q
I think
if then through table
s
automatically our if then is true
then cqi Falls so everyone true and
false so our if then is false if p is
false then Q is true we have here true
if both proposition are false or if then
proposition is true
so for the fourth column Naman
so I'm adding if P then Q will be
represented by the third column which is
if P then Q so don't write it again
and then the conjunction they have the
conjunction symbols
third column and
foreign
column
okay so let's check songs
automatically the result will be false
so when I throw in through so we have
true I false and true so we have false
true and false we have false also true
and false we have foreign
nothing
foreign
foreign
column
if then yeah we need to test the
validity so control and through and
through and through so that is true if
false and false at the false and false
snap n so that will be true also if
false and true so everyone Falls in
through young false and true so we have
also true and then false and false we
have also through
so the resulting conclusions are are all
troopsology
so tautology is a statement that is
necessarily true under any
interpretations
we will consider the argument to be
valid so the argument is valid
[Music]
the argument will be invalid but for
this example valid argument
so um example number one attend which is
if P then q and P therefore Q is a valid
argument
for example number two so let's have the
symbolic form of the given argument so
if P then q and Q therefore
example number one so I thought and Q
therefore P so we will determine if the
given argument is valid or not and to
answer this example so again we need to
have our truth table so
n q
then I'm adding
arguments will be
therefore
okay so first thing to do is
given p and Q to be true or false
table nothing so if that is true and
true so we have here
so that will be
true then false and false at the false
and false nothing and that will be true
also
then for the if P then q and Q so if P
then can nothing happens from the third
column
then I'm adding NQ will be taken from
the Q column
so cute
if P then Q will be represented by the
first column in our conjunction through
table and our Q will be the second
proposition under our two table then we
have the resulting uh conclusion we have
if P then q and Q
so
starting given uh propositions
automatically and so through and through
we have true false and false we have
false through and through we have true
and false we have false also
for p
they are adding if statement will be
taken from the fourth column so that
will be if P then q and Q
so young adding letter piritos adding if
then through table will be represented
by if P then q and Q
then you're adding then statement which
is p
so will be taken from the Pico Loom so
I'm adding if P then Q will be our
conclusion so we have through and
through sorting and doing sat into a
table through and through so the answer
is true
false and through things are through
people Falls and through so we have
through also then through n false
through N4 so again
if P then q and Q times p
so true and false so we have true false
so we have very false and then false and
false so we have F and F we have here
true
I think
resulting conclusion is not a topology a
second consistent in the international
if that will be the case our argument
will be invalid so the argument is
invalid
Target invalid
nothing is
considered to be invalid
okay so example number two
answers so arguments validity so the
argument is invalid
so if P then q and Q are four p
example number three so we have here
our argument so if R then s
and not s therefore R so
negation symbol so symbolic form is
and not s
therefore are
so we will test the validity of this
given argument
okay so again so I think um
so we have the volume of R the column of
s column of f are then s
then we have the column of if R then if
and not s therefore are
and so I'm adding first reference will
be the if then truth table so I'm adding
letter P dito will be our letter r
adding letter Q will be our letter s
P then Q will be if R then f
so we have through through so we have
here true true and false we have here
false false through we have through
false false we have through based on our
little table
and then for the next column young
will be in reference with the trade
column
if r
then s
Eno adding letter you will be
represented by not s
if
is
false
true or false
if our s is false then at s will be true
if our s is true
the negation is false then from false it
will become true
foreign
for the negation of a so young adding
letter Q will be represented by not if
correct conjunctions
automatically Falls
number one
conjunction number two conjunction and
the third conjunction will all be false
applicable language
foreign
false falls falls through
then for the last column
all right
then s and not s so will be referred to
the fourth column is
so it should be in order
okay then an adding letter R so will be
taken from the r column
so I'm adding letter Q will be our
letter r you know adding letter P so
will be the fourth column so if R then s
n that is
conclusion if Arden is and not s
therefore are
through
your number two falls through them
number one falls through your number two
false and true but nothing falls through
I through
false false some false false I through
also
true false so having true false
so if that is true false
the if then conclusion will be false so
again the answer is not a tautology
because marathon is unfortunatic so the
argument will be invalid so the argument
is invalid
example number four we have if M then
not K and not M therefore k
so
example number three Melody m
so they will be the negation of the
original
proposition K and M
so I know
truth is
so if M then that case if then statement
so I'm adding letter P will be
represented by m or adding letter Q will
be presented by not K Peru column
so it is true
nothing will be taken from this column
so I'm adding if P then Q will be
represented by if M then not k
okay so now we have true and false so
you're adding m a true or nothing not k
a false so true and false you have a
conclusion of false
then through and through so my camera
through entry we have here true false
and false so you know false and for
sensible back so we have true also then
Falls in through a thing Falls in
through internet law so Falls in through
the answer is true so when applying some
false pass
okay and then for our fourth column if M
then not K and not m
so we will make use of the conjunction
through people as a conjunctions type of
proposition here
so we have here if M then not a so it
will be
it will replace letter P then you know I
think you will be replaced by not m
so if
M then not K so it will be taken from
the third column then you'll notice
so that will be the negation of the
original M column so true true that will
be false false false false it will be
true through
then you're adding p and Q will be
if M then not K and not M so if
so false false uh answering app and I
false true false so that will be false
also through through that will be true
and true true that will be true
and for the conclusion now for the last
columns
if then table if then truth table so
young adding letter P will be
represented by if M then not K and not m
then I think T will be represented by K
okay if M then not K and not M then
adding K foreign
so we have here if M then not K and not
M therefore K is invalid
and then for the practice exercise
regarding the topic arguments validity
so we will have example number five
practice problems you will determine if
the argument is valid or invalid
and then
comment if the argument is valid or not
in our comment box
and that will be all for this video
Lesson so see you on the next video have
a nice day
5.0 / 5 (0 votes)