GECC103-1D-REINFORCEMENT-UNIT2-LESSON4-LOGIC AND ITS FORMALITY

​LOGIC: where reason meets reality

By Justin Vallinan

INTRODUCTION

Welcome to the Wayground with this lesson created by yours truly, sir Justin Paul D. Vallinan!
Today, you will be participating in this asynchronous class to reinforce further your logical thinking skills!
Your participation will be graded to your class standing!

INTRODUCTION

As you encountered and learned about the needed concepts of logic such as compound proposition, formal logic (rules of inference and rules of replacement), properties of formal logic system (consistency, soundness, completeness), and with the agreed term where you will also be researching all fallacies in logic there is in real-life, we will further apply it as we go along with the Wayground!

INTRODUCTION

Without further ado, let us have our reinforcement activity today!
I will be presenting an orientation of the activity to answer the test along with instruction for you to follow.
by the way, you can have this activity with your notes wide open! Make sure you do all your best for the learning benefit! There could be a bearing to your class standing... :D

ORIENTATION OF ACTIVITY

There are four parts for you to accomplish:
1. Determining a rule from a given argument along its symbolization;
2. Determining a conclusion based on the argument using the rules. of formal logic;
3. Determining the type of fallacy from a given flawed reasoning; and
4. Determining the correct and flawed reasoning from a given debate.

DIRECTION OF ACTIVITY

The first task that you are going to do is to determine the appropriate symbolization to the argument. Then, you will also determine the rule of formal logic used.

Worry not! This type of test is a multiple choice!

Multiple Choice

Argument 1:
"If I save money, then I can buy a bike. I am saving money. Therefore, I can buy a bike."

What is the symbolization for the said argument?

• P ∧ Q , P, therefore Q

• P → Q , Q, therefore P

• P → Q , P, therefore Q

• P → Q , not P, therefore not Q

Multiple Choice

Argument 1:
"If I save money, then I can buy a bike. I am saving money. Therefore, I can buy a bike."

What rule of formal logic is used?

• Modus Ponens

• Modus Tollens

• Material Implication

• Constructive Dilemma

Multiple Choice

Argument 2:
"It's not the case that I will attend the meeting and I will join the party at the same time. What I mean is that, either I will not attend the meeting or I will not join the party."

What is the symbolization for the said argument?

• ¬(M ∨ P) ≡ (¬M ∧ ¬P)

• ¬(M ∧ P) ≡ (¬M ∨ ¬P)

• M ∧ P ≡ (¬M ∧ ¬P)

• M ∨ P ≡ (¬M ∨ P)

Multiple Choice

Argument 2:
"It's not the case that I will attend the meeting and I will join the party at the same time. What I mean is that, either I will not attend the meeting or I will not join the party."

What rule of formal logic is used?

• Contrapositive Law
• Disjunctive Syllogism
• Law of Excluded Middle
• De Morgan's Laws

Multiple Choice

Argument 3:

"If it is hot, then I will drink water. What I mean is that, either it is not hot or I will drink water."

What is the symbolization for the said argument?

• H -> W ≡ ~H v W

• H -> ~W ≡ W v ~H

• H v W ≡ ~H -> W

• ~W -> ~H ≡ H v W

Multiple Choice

Argument 3:

"If it is hot, then I will drink water. What I mean is that, either it is not hot or I will drink water."

What rule of formal logic is used?

• Modus Tollens

• Disjunctive Syllogism

• Material Implication

• Distribution

Multiple Choice

Argument 4:

student Kim: "Either the teacher is strict or the students are noisy."

student Ber: "Yeah... Either the students are noisy or the teacher is strict."

student Ly: "Ber, you just said like what Kim said..."

What is the symbolization for the said argument?

• S ∨ N → N ∨ S

• S ∨ N

• S ∨ N → N

• S ∨ N ≡ N ∨ S

Multiple Choice

Argument 4:

student Kim: "Either the teacher is strict or the students are noisy."

student Ber: "Yeah... Either the students are noisy or the teacher is strict."

student Ly: "Ber, you just said like what Kim said..."

What rule of formal logic is used?

• Commutation

• Disjunction elimination
• Contradiction principle
• Associativity

Multiple Choice

Argument 5:

Mar: "It is not the case that I will not study, my friend."

Tin: "Sooo, you mean you will not study?"

Mar: "What I mean is, I will still study, you numskull."

What is the symbolization for the said argument?

• ¬¬S ∧ ¬S ≡ S

• ¬¬S ≡ S

• ¬¬S ≡ ¬S

• ¬S ∨ S ≡ S

Multiple Choice

Argument 5:

Mar: "It is not the case that I will not study, my friend."

Tin: "Sooo, you mean you will not study?"

Mar: "What I mean is, I will still study, you numskull."

What rule of formal logic is used?

• Modus Tollens

• Double Negation

• Denying the Antecedent
• Modus Ponens

Multiple Choice

Argument 6: (a group of friends deciding on weekends)

Jam: "Okay so. If it rains, then we will watch movies at our home. Okay?"

Mark: "Sure! Then If it is sunny, then we will go to the beach. Deal?"

Group of friends: "Deal!"

Justin: "I see. So either it will rain or will be sunny, we will still either watch movies at Jam's house or go to the beach... Well, I hope it will be sunny by tomorrow..."

What is the symbolization for the said argument?

• P → Q

  Q → R

  ∴ P→R

• (P → Q) ∧ (R → S)

  P ∨ R

  ∴ Q ∨ S

• (P → Q) ∧ (R → S)

  ¬P ∨ ¬R

  ∴ ¬Q ∨ ¬S

• (P → Q) ∧ (R → S)

  Q ∨ S

  ∴ P ∨ R

Multiple Choice

Argument 6: (a group of friends deciding on weekends)

Jam: "Okay so. If it rains, then we will watch movies at our home. Okay?"

Mark: "Sure! Then If it is sunny, then we will go to the beach. Deal?"

Group of friends: "Deal!"

Justin: "I see. So either it will rain or will be sunny, we will still either watch movies at Jam's house or go to the beach... Well, I hope it will be sunny by tomorrow..."

What rule of formal logic is used?

• Constructive Dilemma

• Hypothetical Syllogism

• Destructive Dilemma

• Disjunctive Syllogism

Multiple Choice

Argument 7:

Eun-ho: "Tomorrow, either I will take the bus or I will ride my bike to school."

(the next day)

Eun-ho: "Oh dear! I cannot take the bus today because the drivers are on strike. Oh well,

I will ride my bike then to school."

What is the symbolization for the said argument?

• P ∨ Q , ¬P ∴ ¬Q

• P → Q ∴ ¬P ∨ Q

• P → Q , ¬Q ∴ P

• P ∨ Q , ¬P ∴ Q

Multiple Choice

Argument 7:

Eun-ho: "Tomorrow, either I will take the bus or I will ride my bike to school."

(the next day)

Eun-ho: "Oh dear! I cannot take the bus today because the drivers are on strike. Oh well,

I will ride my bike then to school."

What rule of formal logic is used?

• Disjunctive Syllogism

• Constructive Syllogism

• Hypothetical Syllogism

• Modus Tollens

Multiple Choice

Argument 8:

"I am studying Logic today!"

(a few moments later)

"I am studying Logic or I am playing ML."

What is the symbolization for the said argument?

• P ∨ Q ≡ Q ∨ P

• P ∴ P ∨ Q

• P ∨ P ≡ P

• P ∨ Q, ¬Q ∴ P

Multiple Choice

Argument 8:

"I am studying Logic today!"

(a few moments later)

"I am studying Logic or I am playing ML."

What rule of formal logic is used?

• Disjunctive Syllogism

• Conjunction

• Addition

• Idempotency

Multiple Choice

Argument 9:

Teacher: "you will pass the exam if you studied hard. It only means that you did not study hard in case you will not pass the exam...

Well, It really shows in your exam that your score is not passed."

What is the symbolization for the said argument?

• (P ∧ Q) → R ≡ P → (Q → R)

• P ↔ Q ≡ (P → Q) ∧ (Q → P)

• P → Q ≡ ¬P ∨ Q

• P → Q ≡ ¬Q → ¬P

Multiple Choice

Argument 9:

Teacher: "you will pass the exam if you studied hard. It only means that you did not study hard in case you will not pass the exam...

Well, It really shows in your exam that your score is not passed."

What rule of formal logic is used?

• Contraposition

• Material Implication

• Material Equivalence

• Exportation

Multiple Choice

Argument 10:

Teacher: "If you review your notes, then you will pass the exam."
Mia: "And if you practice solving problems, then you will understand the lessons better."
Leo: "But guess what… some students didn’t pass the exam, or they didn’t really understand the lessons."
Teacher: (nodding) "That means either they didn’t review their notes, or they didn’t practice solving problems."

What is the symbolization for the said argument?

• (P → Q) ∧ (R → S)

  ¬Q∨¬S

  ∴ ¬P ∨ ¬R

• (P → Q) ∧ (R → S)

  P ∨ R 

  ∴ Q ∨ S

• (P → Q) ∧ (R → S)

  ¬P∨¬R

  ∴ ¬Q ∨ ¬S

• (P → Q) ∧ (R → S)

  Q ∨ S 

  ∴ P ∨ R

Multiple Choice

Argument 10:

Teacher: "If you review your notes, then you will pass the exam."
Mia: "And if you practice solving problems, then you will understand the lessons better."
Leo: "But guess what… some students didn’t pass the exam, or they didn’t really understand the lessons."
Teacher: (nodding) "That means either they didn’t review their notes, or they didn’t practice solving problems."

What rule of formal logic is used?

• Hypothetical Syllogism

• Constructive Dilemma

• Destructive Dilemma

• Exportation

DISCUSSION

If you score more than half of it, great job! if not, then you need more exercise.
If you need further clarification, do not hesitate to approach me as I am free and open for tutoring!

DISCUSSION

Let us exercise and deepen our logical thinking as we move on to the second task.

DIRECTION OF ACTIVITY

Your second task is to simply conclude the argument of the skit. It can be a way it is implying something, or wanting to point out by restating the proposition or argument.

Again, worry not! this test is constructed in a multiple choices type!

Multiple Choice

Skit 1:
Anna: "If it rains this afternoon, then the picnic will be cancelled."
Ben: "Look outside—it’s already starting to rain hard."
Anna: "I guess our plan for the picnic won’t work anymore."
Ben: "So what does that mean for us?"

• The picnic will be rescheduled for another day.

• The picnic will be cancelled this afternoon.

• The picnic will be transferred to an indoor venue.

• The picnic will continue as originally planned.

Multiple Choice

Skit 2:
Teacher: "If the homework was submitted on time, then your name will appear on my checklist."
Student: "I checked carefully, and my name is not there on the list."
Teacher: "That means the condition I mentioned did not hold true."
Student: "So what does it imply about me?"

• You forgot to write your name on the paper.

• The teacher misplaced the submitted paper.

• The checklist is incomplete or inaccurate.

• You did not submit the homework on time.

Multiple Choice

Skit 3:
Mom: "Either you washed the dishes after dinner or your sister did."
Kid: "I swear, I didn’t even touch the sink tonight."
Mom: "Well, the dishes are clean, so someone must have done it."
Kid: "Then who should get the credit?"

• The dishes are still dirty in the sink.

• Both of you worked together to wash the dishes.

• Your sister must have washed the dishes.

• Nobody actually washed the dishes tonight.

Multiple Choice

Skit 4:
Coach: "If you train every day, then your stamina will improve. And if your stamina improves, then you will qualify for the marathon team."
Athlete: "I’ve already committed to training daily from now on."
Coach: "That decision has a chain reaction on what comes next."
Athlete: "So where does that leave me?"

• You will surely qualify for the marathon.

• You will improve stamina but fail to qualify.

• You will train daily but not gain stamina.

• You will not qualify for the marathon at all.

Multiple Choice

Skit 5:
Alex: "I’m so relieved—I passed both Math and Science this semester."
Dana: "Wow, you really worked hard for those grades!"
Alex: "Yes, I spent long nights studying for both subjects."
Dana: "So what can I say..."

• You failed Science this semester.

• You passed Math this semester.

• You failed both Math and Science.

• You only retook Math this semester.

Multiple Choice

Skit 6:
Dad: "Congratulations, you passed the driving test this morning."
Son: "Thanks, Dad! That really made me feel proud."
Dad: "So, what can you now claim along with that achievement?"
Son: "Well, I guess I could say that…"

• I passed the test and I sold a car.

• I passed the test but I won’t buy a car.

• I passed the test and I bought a car.

• I passed the test or I will buy a car.

Multiple Choice

Skit 7:
Teacher: "It’s not true that Maria didn’t win the contest yesterday."
Classmate: "Wait, that sounds a little confusing."
Teacher: "Let’s put it in simpler terms. If it’s not true that she didn’t win, then what does it mean?"
Classmate: "So the real outcome is…"

• Maria actually lost the contest.

• Maria actually won the contest.

• Maria actually missed the contest.

• Maria actually skipped the contest.

Multiple Choice

Skit 8:
Teacher: "For your grade, you need to submit both your essay and your final project."
Student: "So I can’t just pick one and skip the other?"
Teacher: "Correct—you have to complete both requirements."
Student: "Then saying it in reverse order should mean the same thing, right?"

• You must submit the essay and the project.

• You must submit the project and the essay.

• You must submit the project but not the essay.

• You must submit the essay but not the project.

Multiple Choice

Skit 9:
Security Guard: "It’s not true that both the library and the laboratory are open tonight."
Student: "So, that means at least one of them isn’t available?"
Guard: "Exactly. It doesn’t say both are closed, just that both aren’t open together."
Student: "So what’s the best way to state that?"

• Either the library is closed or the lab is closed.

• Both the library and the lab are still open.

• Neither the library nor the lab is open.

• The library is open whenever the lab is open.

Multiple Choice

Skit 10:
Driver: "If the train departs on time and the tracks are clear, then the passengers will arrive early."
Commuter: "So are you saying that the train leaving on time guarantees early arrival?"
Driver: "Not exactly. What I mean is, ..."

• If the tracks are clear, then the train must depart on time.

• If the train departs late, then the passengers will not arrive early.

• If the train departs on time, then if the tracks are clear, the passengers will arrive early.

• If the passengers arrive early, then the train departed on time and the tracks were clear.

DISCUSSION

That's great! Great job honing your logical thinking up to this point. I hope you scored more than half of it. If not, then, as I said, do not hesitate for tutoring!~
It will not be thrilling if we do not take into account certain fallacies, or flawed reasoning.

DIRECTION OF ACTIVITY

With that, your third task is to read carefully the conversation and determine the flaw of the conversation presented in the next slide. Afterwards, answer what is being asked.

that is to say, it is still multiple choice!

Multiple Choice

1. Student B says: “I forgot my gadget yesterday and still got distracted — so banning gadgets won’t help anyone.”
What is the flaw?

• False analogy

• Hasty generalization

• Denying the antecedent

• Circular reasoning

Multiple Choice

2. Student C says: “If banning gadgets makes us more focused, then since I’m focused, it means gadgets are already banned.”
What logical error is this?

• Affirming the consequent

• Denying the antecedent

• False cause

• Equivocation

Multiple Choice

3. Student D says: “My cousin is a top student and he always uses gadgets, so gadgets must make you smart.”
What is wrong here?

• Hasty generalization

• Slippery slope

• Appeal to ignorance

• Straw man

Multiple Choice

4. Student E says: “If we allow gadgets today, tomorrow people will start playing games, then cheating, then no one will study at all.”
What reasoning error is used?

• False dilemma

• Slippery slope

• Composition fallacy

• Appeal to pity

Multiple Choice

5. Student F says: “The principal says gadgets are harmful, so it must be true.”
This is best described as:

• Appeal to authority

• False cause

• Ad hominem

• Begging the question

Multiple Choice

6. Student G says: “Last time he banned soft drinks, and some students still got hyper, so clearly banning doesn’t work.”
Which fallacy is this?

• False cause

• Hasty generalization

• False analogy

• Equivocation

Multiple Choice

7. Student H says: “If you’re against gadgets, you’re basically saying you don’t care about students learning at all.”
What flaw is present?

• Straw man

• False dilemma

• Ad hominem

• Appeal to emotion

Multiple Choice

8. Student I says: “I think all students who use gadgets in class are irresponsible, because I once saw a classmate scrolling during a lesson.”
Which fallacy is committed?

• Composition fallacy

• Hasty generalization

• False cause

• Complex question

Multiple Choice

9. Student A says: “If gadgets distract students, then banning them will make us all more focused.”
What assumption makes this flawed?

• Equivocation on the term “distract”

• Assuming banning is the only solution

• Composition fallacy

• Post hoc fallacy

Multiple Choice

10. In the whole discussion, which statement best represents an ad hominem if it were added?

• “You only argue for gadgets because you’re lazy.”

• “Gadgets might have benefits in certain contexts.”

• “Banning gadgets could help but might not be sufficient.”

• “We should ask students how they use gadgets productively.”

DISCUSSION

Wonderful! We are getting further and further! Let us make our logical thinking in line as we now take in to the last task: reviewing the debate!

DIRECTION OF ACTIVITY

Your last task is to analyze the whole debate and answer what is being asked.

Here is the twist! It is still multiple choice!!!

ACTIVITY: DEBATE

Topic: “Should the university ban gadgets inside classrooms?”

Multiple Choice

1. Compare Anna’s and David’s arguments. Both use a similar logical pattern. What makes Anna’s argument potentially stronger than David’s?

• Anna’s premises are more universally true, while David’s depend on an assumption.

• Anna’s conclusion is simpler, while David’s is more complex.

• Anna’s reasoning involves fewer steps, so it must be correct.

• Anna uses cause-and-effect, while David uses correlation.

Multiple Choice

2. In Ben’s argument about students complaining, Clara pointed out a flaw. What was the problem with Ben’s reasoning structure?

• He denied the antecedent.

• He affirmed the consequent..

• He failed to state a premise.

• He used circular reasoning.

Multiple Choice

3. Look at Ben’s use of De Morgan’s Law: “It’s not true that gadgets are both helpful and harmful, so they must be either not helpful or not harmful.” Which issue weakens his reasoning the most?

• The equivalence he used does not logically exist.

• The interpretation ignores gadgets’ mixed effects.

• He confused disjunction with conjunction.

• The statement contradicts Anna’s earlier point.

Multiple Choice

4. If you were the moderator, which of the following arguments would you consider the least sound, even if it looks valid in form?

• Anna’s argument that distraction leads to loss of focus.

• David’s claim that banning harms education if gadgets improve learning.

• Ben’s claim that complaints prove banning is harmful.

• Clara’s statement that two opposite claims cannot be true at the same time.

Multiple Choice

5. Considering consistency, soundness, and completeness, which participant’s reasoning was the most reliable overall?

• Anna, because her argument had a clear structure and a plausible premise.

• Ben, because he challenged assumptions and used laws of logic effectively.

• David, because his conclusion about harm was strong and forceful.

• Clara, because she evaluated others’ reasoning and pointed out contradictions.

Multiple Choice

6. Suppose you want to support Anna’s side but avoid her weakness of overgeneralization. Which of the following would be the strongest newly constructed argument?

• If some gadgets distract students, then all gadgets should be banned.

• If certain gadgets distract students, then those specific gadgets should be regulated in class.

• If students sometimes lose focus, then banning all gadgets will solve the issue.

• If gadgets exist, then distraction is inevitable.

Multiple Choice

7. Imagine you want to strengthen David’s reasoning. Which revised version of his argument best avoids a weak premise?

• If gadgets improve learning in all subjects, then banning them hurts education.

• If gadgets exist, then banning them destroys education.

• If gadgets can improve learning when used responsibly, then banning them limits opportunities.

• If gadgets distract students, banning them must help.

Multiple Choice

8. Ben misused complaints as proof. How could you reconstruct his claim into a logically stronger argument?

• If banning gadgets consistently lowers test performance, then it harms education. Evidence shows performance drops after banning. Therefore, banning harms education.

• If students complain, then banning is harmful. Students complain. Therefore, banning is harmful.

• If banning gadgets happens, then students complain. Students complain. Therefore, banning happens.

• If banning gadgets occurs, then the weather changes. The weather changed, so banning must have occurred.

Multiple Choice

9. Construct a counter-argument to Anna’s first claim by using the same form she used, but in favor of allowing gadgets. Which option does this best?

• If gadgets improve focus, then students learn better. Gadgets improve focus. Therefore, students learn better.

• If gadgets exist, then students are distracted. Gadgets exist. Therefore, students are distracted.

• If gadgets are harmful, then students fail exams. Students fail exams. Therefore, gadgets are harmful.

• If gadgets are banned, then students succeed. Students succeed. Therefore, gadgets are banned.

Multiple Choice

10. If you were tasked to design a final statement as the moderator, which closing best shows a complete and logically consistent conclusion?

• Because some gadgets distract, all gadgets should be banned.

• Because banning may both help and harm, the truth cannot be determined.

• Because valid arguments need both correct form and true premises, the debate shows that evidence matters as much as logic.

• Because students are divided, the university should do whatever the majority wants.

DISCUSSION

Excellent! You made the end of the reinforcement activity!
Surely it is tiring just by thinking and reasoning out certain arguments.

Yet, it is for the benefit of your learning to avoid being ignorant towards people around you.

By these content, I have one very simple task to end our learning.

CLOSING

Before anything else, I want you to write in any paper your own or searched catchphrase about logic.
Afterwhich, have your own selfie along with the catchphrase and submit it to our GCR.
be reminded that next meeting will be your performance task: IMPROMPTU DEBATE.