Attheendofthelessonthestudentsshouldbe ableto: 1.definecategoricalsyllogism; 2. differentiate Euler's Diagram from Venn Diagram; 3. enumerate the different set of rules in categoricalsyllogism;and 4. determine the validity of categorical syllogism.
Thelearnerdemonstratesunderstandingofthe key concepts of propositional logic; syllogisms andfallacies.
Are there any absentees for today?
(In the name of the Father, the Son, and the Holy Spirit, Amen.) Good morning Ma’am! (The students will pick-up the pieces of papers and put it on the trash can and arrange their chairs.) ThankyouMa’am! NoneMa’am,Everybodyispresenttoday. A. Reviewing previous lesson or presenting the new lesson Last meeting, we discussed about the differenttypesoftautologiesandfallacies. Igiveyouanassignmentright? Who wants to answer the assignment on theboard? Yes,________________
Yes,ma'am! (Thestudentswillraisetheirhands.) Draw a conclusion! 1. If I pass the final exam, I will graduate. I
That’s correct!
Check the assignment of your seat mate. Two points for each correct answer. Who got a perfect score?
Verygood!Allofyougotaperfectscore. Now, how important is your knowledge about tautologies and fallacy in real-life situations?
graduated. Therefore, I passed the exam.
2. I will go to La Union, I will eat “Halo-Halo” de Iloko. If I eat “Halo-Halo”, I gain weight. Therefore, I will go to London
3. Rachel and Paulo will be at a concert. Rachel was at the concert. Therefore,… Paulowasatthe concert.
4. If a person is an engineer, then that person has a college degree. Dennis does not have a college degree. Therefore, Denniswasnotanengineer.
5. If I am irritated or angry, I cannot concentrate. I can concentrate. Therefore, Iwasnotirritatedor angry. (All students will raise their hands.)
B.Establishing a purpose for the lesson
Class, kindly read the content standard and performance standard.
(Thestudentswillraisetheirhands.)
It will help us prove what is really true and differentiateitfromthefalseone.Atruthtable will determine if my classmates, relatives, brothers, sisters, mother, father, and many more words, comfort, and promises are tautologyorfallacy.
CONTENTSTANDARD:
The learner demonstrates understanding of the key concepts of propositional logic; syllogismsandfallacies.
PERFORMANCESTANDARD:
Thelearnerisabletojudiciouslyapplylogicin real-lifearguments.
For us to be properly guided in discussing our topic, let me first present to you our objectives for today’s lesson.
1st rowkindly read the first objective.
Thankyou! 2ndrowkindlyreadthefirstobjective. Thank you!
3rd row kindly read the second objective. Thank you! Everyone read the last objective. Thankyou!
Beforewestartdiscussingourlesson.Let's have a brain teaser! All you have to do is to answer it faster and correct. Are you ready? MECHANICS: Using the rubrics Correct answer = 8 points Discipline=2points
Attheendofthelessonthestudentsshouldbe ableto: 1.definecategoricalsyllogism; 2. differentiate Euler's Diagram from Venn Diagram; 3. enumerate the different set of rules in categoricalsyllogism;and 4. determine the validity of categorical syllogism. Yes,ma'am.
(Thestudentswillraisetheirhands.) Acategoricalsyllogismisadeductiveargument consisting of exactly three categorical propositions(twopremisesandaconclusion).It issaidto be validifand only iftheconjunction ofthepremisesimpliestheconclusion.
(Thestudentswillraisetheirhands.)
Therearefourwaystodeterminethevalidityof categorical syllogisms: check the form against the list of valid arguments; useVenn diagrams;
Definitely! Beforewefinallyproceedwiththelesson, you should be able to recall how to construct a Venn diagram to represent a given statement.
Activity 1: A Visit to Historical Place
Directions: I will group you into three. To acknowledge your answer, just clap your hands and first group who claps will be entertained. Our counting starts at the back.
MECHANICS:
Using the rubrics
Creativity = 5 points
Correct answer = 8 points
Discipline=2points
Mr. Sandoval wants his children to instill thevalueofpatriotismtohisfourchildren. This summer, he is planning to visit with his family one historical place in the Philippines.Hehasnotyetdecidedifthey will go to Corregidor Island in Bataan or will visit the Emilio Aguinaldo Shrine in Kawit, Cavite. To help him decide, he asked his four children which of the two historical places they want to explore. Their answers are summarized in a Venn diagrambelow:
draw a picture of the premises using Euler’s diagrams;andlastly,useasetofrules. (The students are getting ready for another activity.)
(Thestudentsstartcounting.)
Activity 2: What’s that Prove? Group yourselves into four. Each group must have 6-8 members. Using your reasoning, determine whether the following are VALID or INVALID. Justify youranswers.Iwillprovideacartolinaand pentelpen. You may use illustrations to supportyourclaim. MECHANICS: Using the rubrics Creativity = 5 points
answer = 8 points Discipline=2points Let'sstartprovingyourworth.Imean,the validityofthearguments. 1.Godislove;loveisblind.Therefore,God is blind.
(Thestudentsfeelsexcited.) (Thestudentschoosetheirgroupmembers.) (Thestudentswillreact.) 1. INVALID. Commits the policy of weuivocation,becausetheword"love"isbeing used in different senses in the first two premises.
2. All hardworking students are friendly. No friendly student violates school policies. Therefore, no violator of school policies is a hardworking student.
3. All monkeys eat banana, Nestor eats banana. Therefore, Nestor is a monkey.
4. All frogs can jump, horses can jump. Therefore, a horse is a frog.
5. All SHS students are honest. Some creative thinkers are SHS students. Therefore, some creative thinkers are honest.
6. All birds can fly, airplanes can also fly. Therefore, an airplane is a bird.
7. Laila has a heart; banana also has a heart. Therefore, Laila is a banana.
8. All pigs have 4 legs, tables have 4 legs. Therefore, a table is a pig.
9.Angelicaisbeautiful,amountainisalso beautiful. Therefore, Angelica is a mountain.
10.All donors for the “Pasko with Ate and Kuya” are successful persons. No successful persons are lazy persons. Therefore, no lazy persons are donors for the “Pasko with Ate and Kuya”.
Guide Questions:
1. How did you find the activity?
2. VALID. AEE-4 3. INVALID. AAA-2 4. INVALID. AAA-2 5. VALID. AII-1 6. INVALID. Commitsthefallacyofequivocation becausetheword"fly"isbeingusedindifferent sensesonthefirsttwopremises. 7. INVALID. Commitsthefallacyofequivocation because the word "heart" is being used in differentsensesinthefirsttwopremises. 8. INVALID. AAA-2 9. INVALID. AAA-2 10. VALID. AEE-4
(Thestudentswillraisetheirhands.) We find the activity engaging, fruitful and we enjoyansweringit. (Thestudentswillraisetheirhands.) Yes.
2.Wereyouabletodeterminethevalidity of each statement?
3.Whatstrategiesormethodsdidyouuse to justify the validity or invalidity of each statement?
4.Didyouconsiderthetruthvalueofeach propositioninthesyllogismstodetermine each validity? Why?
5. How can we determine if the statementsjustlikepresentedarevalidor not?
(Thestudentswillraisetheirhands.) Weusedifferentstrategieslike......
(Thestudentswillraisetheirhands.) Yes,because...
(Thestudentswillraisetheirhands.) It is valid if both arguments are true and it is invalidiftheargumentsdeliveredfallacy.
(Thestudentswillraisetheirhands.) Validityis... E. Discussing new concepts and practicing new skills #2 Activity1.1 Isn't it? Directions: In this activity, using the same group. You are assigned on different activitiesbellowandpresentitintheclass using tiktok dance moves. May I have the group leaders and pick a number here in front,toidentifywhichactivityyouwilldo. MECHANICS: Usingthesamerubrics.
6.Inyourownwords,whatisvalidity?
cheaters.
Activity2: Determine the validity of the following categorical syllogisms using the Venn diagram. 1.AllMareP. Some S are M. Some S are P. ∴ 2.NoPareM. Some S are M. Some S are not P. ∴ 3. Some M are not P. AllMareS. SomeSarenotP.∴ 4.SomePareM. Some S are M. No S are P. ∴ 5. All P are M. No M are S. NoSareP.∴
Activity3. Identify the terms, mood and figure then determine its validity by looking at the table of valid categorical syllogisms. Write your answer in the table and use the format given below:
1. Some of the wastes collected in factories are radioactive. No wastes collectedin factoriesaredumpedintothe ocean.Therefore,someradioactivewastes are dumped into the ocean.
2. All pliers are tools and all screwdrivers are tools. Therefore, all pliers are screwdrivers.
3. All contagious diseases should be subject to mandatory testing. COVID-19 is contagious. Therefore, testing for COVID19 should be mandatory.
4. All working students have no laptops and all successful students are persons who have laptops. Thus, all working students are successful students.
5. All sea vessels that sunk are unsafe vessels. All well-maintained vessels are safe vessels. Therefore, no vessels that sunkarewell-maintained.
2
Middle Term Wastes collected infactories.
Major Term Screwdrivers
Minor Term Pliers
Middle Term Tools
3
Major Term Deseases subject to mandatory subject.
Minor Term All deseases identical to COVID-19
Middle Term Contagious deseases
4
Major Term Successful students
Minor Term Workingstudents
Middle Term Students who havelaptops.
AA A 2 Invalid
AA A 1 Valid
AE A 2 Invalid
5
Major Term Well maintained vessels. EA E 2 Valid
Minor Term Vesselsthatsunk.
Middle Term Safevessels.
Activity4: Determine the validity of the following categorical syllogisms using any method.
1. All educational games should be encouraged.Notallgamesareeducational games.Therefore,notallgamesshouldbe encouraged.
2.Allleadersaregoodcommunicators.All
1. VALID. AII-1
good communicator people are creative. Therefore, all creative people are leaders. 3.Allgoodstudentsshowloveforcountry. Somestudentswhoshowloveforcountry are respectful. Therefore, all respectful studentsaregoodstudents. 4. All prisms are plane figures. All cubes are prisms. Therefore, all cubes are plane figures. 5. No Quezonians are lazy. Most lazy people have low income. Therefore, no Quezonianshavelowincome.
Whogotitallcorrect?
Very good. Some of you got the perfect score.
Passitforward.
SareP.
2.AllMareP.SomeMareS.Therefore,someS areP.
3. All P are M. Some S are not M. Therefore, someSarenotP.
4.AllMareP.AllSareM.Therefore,AllSareP.
5. Some M are not P. No M are S. Therefore, someSareP.
6. No P are M. Some M. are S. Therefore, all S areP.
7. Some M are P. All S are M. Therefore, no S areP.
8.NoPareM.AllMareS.Therefore,Sarenot P.
9. No P are M. All S are M. Therefore, some S arenotP.
10. SomePareM.NoMareS.Therefore,allS areP.
(Thestudentswillraisetheirhands.) Yesma'am! (Thestudentswillpasstheirworkinfront.)
4.Quantity
5.Quality 6. a.Majorterm, b.MinorTerm, c.Middleterm 7. a.Majorpremise, b.Minorpremise 8.Mood 9.figure
DIRECTIONS: Construct your own syllogisms that satisfy the following conditions:
10.256,15,9
1. An AII-3categoricalsyllogismwiththese terms: major: creative people; minor: brave people; middle: musicians.
2.Anunconditionallyvalidsyllogisminthe
Yes,ma'am! (Thestudentswillpasstheirwork.)
first figure with a universal negative conclusion and these terms: major: Academic students; minor: ICT students; middle: TVL students.
3.Anunconditionallyvalidsyllogisminthe fourth figure having two universal premisesandtheseterms:major:Filipinos; minor: selfish; middle: hospitable.
4.AvalidsyllogismhavingmoodAOOand theseterms:major:entrepreneurs;minor: risk-taker people; middle: persistent people.
5. A valid syllogism in the first figure having a particular negative conclusion and these terms: major: SHS subjects; minor: fun and challenging subjects; middle:researchsubjects
H. Making generalizations and abstractions about the lesson
Get a clean bond paper and answer this quietly.
ACTIVITY:Here'stheCatch!
A.Pleasereadthesentencescarefullyand fill in the missing word/s by writing your answerontheline/sprovided.
1. A ________________ is a proposition thatrelatestwoclassesorcategories.
2. A ________________ is a deductive argumentinwhichaconclusionisinferred fromtwopremises.
3. A ________________ is an argument consisting of exactly three categorical
propositions (two premises and a conclusion) in which there appear a total ofexactlythreecategoricalterms,eachof whichisusedexactlytwice.
4. The ________________of a categorical propositioniseitheruniversalorparticular
5. The ________________of a categorical proposition is either affirmative or negative.
6.TermsoftheCategoricalSyllogism
a. ________________is the predicate of theconclusion.
b. ________________is the subject term oftheconclusion.
c. ________________is the term that appears in both premises but not in the conclusion.
7.PartsoftheCategoricalSyllogism
a. ________________contains the major term.
b. ________________contains the minor term.
8. The ________________of a categorical syllogism consists of the letter names of the propositions that make it up. Moods are defined as the arrangement of the premises according to quantity (universal or particular) and quality (affirmative or negative).Inotherwords,wecansaythat mood is determined by the type of standard form categorical propositions of
4.Quantity 5.Quality 6. a.Majorterm, b.MinorTerm, c.Middleterm 7. a.Majorpremise, b.Minorpremise 8.Mood
thesyllogismcontains.
9. The ________________of a categorical syllogism is determined by the location of thetwooccurrencesofthemiddletermin thepremises.Fourdifferentarrangements are possible. If we let S represent the subject of the conclusion (minor term), P the predicate of the conclusion (major term), and M the middle term, and leave out the quantifiers and copulas, the four possible arrangements may be illustrated asfollows:
10.Sincethereare4figuresand64moods, there are _____________________ categorical syllogisms. Only ___________________are unconditionally valid and ________________ are conditionallyvalidforms.
Areyoudone? Okay,passyourwork. Whocandefinecategoricalsyllogisms? Yes,__________. Exactly! Whatistheimportanceofdeterminingthe validityofacategoricalsyllogism? Yes,__________.
9.figure 10.256,15,9 Yes,ma'am! (Thestudentswillpasstheirwork.)
(Thestudentswillraisetheirhands.)
Acategoricalsyllogismisadeductiveargument consisting of exactly three categorical propositions(twopremisesandaconclusion). (Thestudentswillraisetheirhands.) Theimportanceofdeterminingthevalidityofa
Fantastic!Verywellsaid. Now, how can you apply different methodsinvalidatingcategoricalsyllogism inreallifesituations? Yes,________.
That'sgreat! Do you any questions, clarifications, violent reactions, and additional informations?
structure of this argument. Meanwhile a categorical syllogism is sound if and only if it is both valid, and all of its premises are actually true. (Thestudentswillraisetheirhands.) I can apply my learning in this lesson through mentallyidentifyingtruthfromlies.
Nonema'am.
I. Evaluating learning
Preparedby: MechelleGarciaQuinto BSEDMathematics-4Student
Constructing plans is always better than making rash decisions. Just like in the teaching profession,thereshouldbeanaheadplanforeverylessontodeliveritclearlytothestudents. And in return, the students will get the knowledge correctly. While doing the lesson plan I realizedthatitwasnotaseasyasitseems.Therearelotsofactivitiesthatyouwantedtoinsert in the lesson but then there is alimited time indoing so. So, for me to implement my lesson planeffectivelyandpurposefully,Iwillplanactivitiesanddiscussionswithinthetimeframebut at the same time I will make sure that my students will understand the importance of the lessononceitends.Allinallitwasenjoyableandveryinspiringasafutureeducator.