Part A

Question 1

  1. a) Valid deductive arguments; strong inductive arguments

Deductive arguments are valid only when their premise successfully guarantees their conclusions by providing an overwhelmingly strong support that truth in the premise makes it impossible for the conclusion to be fallible whereas an inductive argument is strong when the truth in its premise is so strong as to increase the probability of its conclusion being true.

  1. b) Weak inductive arguments; invalid deductive arguments

An inductive argument is weak when the strength of its premise’s truth does little to increase the likelihood of the truth of its conclusion whereas a deductive argument is invalid when the premise does not fully guarantee a factual relation with the conclusion.

  1. c) Arguments; explanations


An argument is the basis with which a reason seeks to logically support allegations made by a conclusion answering the question ‘how?’ whereas an explanation forms the basis with which a reason seeks to aid in the understanding of the origins of specific information represented in a conclusion.


Question 2

The audience will applaud heartily if the show is good. If the show is good, the director will be pleased. If the show is good the director will be pleased.

Question 3


1- Mandie hopes to take either metaphysics or epistemology.

2- She will take epistemology only if Professor Holms teaches the class.

3- It seems that Mandie will be taking metaphysics, since I just heard that Professor Holms will be on leave next term.









1- The crime was committed by someone very strong. George is singularly weak.

2- So, George cannot be the culprit. Now, either George of Janice is guilty of the crime.

3- So, Janice is guilty of the crime.









1- If we take in hand any volume; of divinity or school metaphysics, for instance; let us ask, “Does it contain any abstract reasoning concerning quantity or number?” No.

2- “Does it contain any experimental reasoning concerning matter of fact and existence?” No.

3- Commit it then to the flames; for it can contain nothing but sophistry and illusion.


Question 4

  1. a) The Dean threatening to disband the Humanities division is an informal fallacy. The powers to disband or reconstitute a faculty lie with the governing body of an institution with Deans playing a largely administrative role. It logically follows that the Dean cannot disband the Humanities division.
  2. b) There are many things that are invisible to the human eye that we still know exist like air. The existence of something is not determined by a person’s ability or lack thereof to perceive it. The statement is therefore an informal fallacy.
  3. c) Using the players’ ages as a basis for determining their team’s age is an informal fallacy. Social institutions like teams and clubs experience continuous changes in their patronage from new registrations and retiring of old members. Basing the assessment of an institution’s age by looking at the average ages of its patrons would result in an incorrect figure hence making the statement an informal fallacy.
  4. d) The truth of a theory is not determined by the race, sex, creed or nationality of the person advancing it. Theories are advanced based on findings derived from a battery of rigorous. Nazi’s hatred for Jews made them discredit all advancements they made to the extent of trying to take credit of some as they considered themselves the superior race. The truth of Einstein’s theory of special relativity could therefore only be disapproved through logical experiments to ascertain the validity of his findings and not because of his race making the statement an informal fallacy.


Question 5

  1. a) The new candy bar, Chocolate Almond Yummies, are said to provide similar nutritional and energy values as fruits. Since fruits have many attributes that are good for your health, and the same nutritional and energy values can be gotten from the new candy bar, it stands to reason that the new candy bar can be an effective substitute for fruits. This makes a strong argument that the new candy bar should also be good for your health.
  2. b) Human beings have managed to create complex machines that handle complex tasks accurately and efficiently and they use them to do the bulk of their daily work. These machines connect with each other so intricately through the internet that their access and operation can be done seamlessly from remote locations. Since the universe acts in much the same way as the creations of man but only on a larger scale, it stands to reason that whoever or whatever created it must have had similar characteristics to man with regard to creativity and design with the difference being in the scale of abilities and inhibitions and resources. This is the basis for proposing the existence of a deity and his similarity to man.
  3. c) The difference between a fetus and a person is time. It begs the argument that they have the same rights and should be treated equally and offered the same degree of protection. It therefore proposes that the law allows protection of a fetus from the date of conception to develop naturally into a person and not to abort it.

.Question 6

  1. a) Probability of picking a “sad one”= Number that like Toronto Maple Leafs: Total club membership

Total club members= 100

20 like the Toronto Maple Leafs (they are “the sad ones”)


=20% Probability that the member selected is “a sad one”

  1. b) =Probability of selecting “a puzzled one”+ Probability of selecting “a faithful one” + Probability of selecting “a nostalgic one”


=50% probability that the member selected is either “a puzzled one,” “a faithful one,” or “a nostalgic one”

  1. c) = Probability that the member selected is a “a righteous one”* Probability that the member selected is a woman

= 34%*40%

=13.6% Probability that the member selected is a woman who is “a righteous one”

  1. d) =Probability that first selection is “faithful ones”+ Probability that second selection is “faithful ones”

First selection total membership= 100

Second selection total membership= 99

= 22%+21%

= 43% probability that both are “faithful ones”


  1. e) Probability that the first one selected is “a sad one”+ Probability the second one selected is “a righteous one”

First selection total membership= 100

Second selection total membership= 99

= 20%+34%

=54% Probability that the first one selected is “a sad one” and the second one selected is “a righteous one”

Question 7

= Probability of one reaching his tent*5 people

= 20%*5

= 100% Probability that each one reached their own tent

Question 8

  1. a) Eating bad clams is a sufficient condition to cause one to fall ill. Since eating bad clams is not the sole trigger of illness, it means one can fall ill regardless of whether they ate bad clams or not making the eating of bad clams only a sufficient condition for triggering illness.
  2. b) Since every force exerted experiences an equal but opposite force in matter’s attempt to maintain equilibrium, the stretching of a spring is both a sufficient and necessary condition for it to exert an opposing force in its attempt to maintain its structural integrity and balance.
  3. c) Heat causes metals to expand while they retain their original form in its absence and is therefore both a necessary and sufficient condition to create an expansion in the physical structure of a solid iron bar.


  1. d) A gun can only fire if its trigger is pulled. Pulling the triggers of a gun is therefore a necessary cause for it to fire. Guns have however been known to fire accidentally without their triggers being pulled especially those with hair triggers that can go off from a bump or tap. Pulling the trigger is therefore not the sole necessary condition for a gun to fire.
  2. e) Litmus paper only turns red when in contact with acids making acids a necessary and sufficient condition for the reaction since the absence of an acid or presence of other non acidic liquids would not turn litmus paper red.

Question 9

Method of Agreement

Suppose four candidates fail because the teacher did not receive their final papers. The first claims he submitted his report online a whole day before the deadline, the second around fifteen hours before, the third five hours and the fourth one submitted his with two hours to spare. He however received all submissions made 24 hours before the deadline making him conclude that there might have been a problem with his mail server or inbox.

Method of Difference

Suppose only two candidates fail but claim to have submitted their assignments from the school library but one’s assignment reached the teacher while the other’s did not and they were using different types of computer, the teacher can conclude that one might have been undelivered because of his computer’s incompatibility with the school library’s network.

Method of Residues

Suppose the teacher in his prior collection of assignments via email has already established that certain computers that students use are unable to access mail functions while on the school’s library network. Today the teacher can accept a late submission from a student who claims they used a similar computer on the school’s library network when making their submissions and give the candidates a grade making them pass the course.

Concomitant Variation

Suppose the teacher receives four complaints: the first sent his assignment using a modem connection and his assignment was received but late, the second used a pc in the school’s library and his assignment was delivered multiple times, the third used a mac and his assignment never got delivered completely while the last one used the library’s computers and his assignment was delivered as a corrupted file. The conclusion again is that the library’s network is unreliable and can cause hiccups in sending assignments.

Question 10

Name Harry Job Kerry Grant
Math 50 89 65 14
Geography 60 74 35 20
Physics 36 58 59 85
Biology 20 35 87 99
Totals 166 256 246 218



Mean helps to establish the point of central tendency, which helps determine whether the exam was set in a standard manner. Optimal tests have more candidates distributed at the mean.


Medians show the mid point in a data set. This also mostly falls within the mean pool and can further help define the central tendency point.


Mode is essential in determining which entities have an equal or similar capability and is a crucial determinant of groupings.

Question 11

If you include garlic in a dog’s food, then the dog will live longer than those that do not have a regular intake of garlic.

If you fortify your dog’s meals with garlic, the dog will be healthier and happier. Animals live longer due to good health and good management of stress, which increases their happiness levels and effective well-being. This is a better hypothesis because it relates garlic intake to specific longevity triggers.

Question 12

  1. a) False
  2. b) True
  3. c) False
  4. d) True
  5. e) True
  6. f) True
  7. g) False
  8. h) True
  9. i) False
  10. j) True
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