1. Inference is the mental process of deriving a new judgment based on relating several known premises. There are two types of inference: immediate and mediate. 2. A syllogism is the logical form of a mediate inference where a conclusion is drawn from two premises related by a middle term. It involves three terms: a major term, minor term, and middle term. 3. There are four basic figures of the syllogism depending on where the middle term is located among the three terms. Each figure has valid moods depending on whether the premises and conclusions are universal or particular in quality.

1. INFERENCE
AND
SYLLOGISM

2.  It is the mental activity whereby starting with several
judgments which we relate to one another, we arrive
at a new judgment which necessarily follows from
the preceding ones.
 Every reasoning process, involves a number of
previously known truths. These truths are called
premises. The reasoning process also involves the
knowledge of a new truth (the conclusion).

3.  It is the drawing of a conclusion from one or more
premises. There are 2 kinds of inference:
immediate and mediate.
 Immediate – when a conclusion is drawn from only
one premise.
 Mediate – when a conclusion is drawn from two
premises.
 The mental product of inference is called an
argument: The external expression of which is
called a syllogism.

4.  It is the logical process in which the premises relate
two terms with a third (middle), and the relationship
is expressed in the conclusion that either unites
(affirmative) or separates (negative) the first two
terms
 It is an inference that draws the conclusion in an
absolute manner. Here, when the first 2 propositions
are posited as true, the third must also be true.
 All animals are substances.
But, a dog is an animal.
Therefore, a dog is a substance.

5.  It is an inference which concludes with certainty,
affirming or denying a statement, from the
affirmation or denial of another.
 If the students plagiarize, then they should be
punished.
The students plagiarize.
Therefore, they should be punished.
 Either you pass the test, or you fail.
You pass.
Therefore, you did not fail.

6.  All humans are mortal.
All Filipinos are humans.
Thus, all Filipinos are mortal.
 Major premise: All humans are mortal.
Minor premise: All Filipinos are humans.
Conclusion: All Filipinos are mortal.
 Major term (T) – predicate of the conclusion
Minor term (t) – subject of the conclusion
Middle term (M) – found in both premises.

7.  Figure 1
 M T
t M
Thus, t T
 SUB-PRE
 Some scholars are wide-readers.
Some Filipinos are scholars.
Thus, Some Filipinos are wide-readers.
 III-1

8.  Figure 2
 T M
t M
Thus, t T
 PRE-PRE
 All great scientists are college graduates.
Some professional athletes are college
graduates.
Thus, some professional athletes are great
scientists
 AII-2

9.  Figure 3
 M T
M t
Thus, t T
 SUB-SUB
 All artists are egoists.
Some artists are paupers.
Thus, some paupers are egoists.
 AII-3

10.  Figure 4
 T M
M t
Thus, t T
 PRE-SUB
 No gamblers are quitters.
All quitters are losers.
Thus, no losers are gamblers.
 EAE-4

11. 1. No heroes are cowards.
Some soldiers are cowards.
Thus, some soldiers are not heroes.
2. All sacrifices are rewarding.
Some acts of cheating are rewarding.
Thus, all acts of cheating are sacrifices.
3. All pilots are risk-takers.
Some pilots are not happy-go-lucky.
Thus, some risk-takers are not happy-go-lucky.
4. No nuclear-powered submarines are commercial
vessels, so no warships are commercial vessels,
since all nuclear-powered submarines are
warships.

12.  Some animals are two-legged.
All people are animals.
Thus, all people are two-legged.
 All animals are mortal.
Some animals are dogs.
Thus, some dogs are mortal.

13. 1. There must only be 3 univocal terms, each of
which occurs twice but not in the same
proposition.
A father is a male parent.
The Holy Pope is a father.
Thus, the Holy Pope is a male parent.
*Fallacy of Equivocation
All flowers are beautiful.
All roses are flowers.
Thus, all roses are beautiful.

14. 2. The middle term must not occur in the
conclusion.
A goddess is a female.
A goddess is a deity.
Thus, a goddess is a female deity.
*Fallacy of Misplaced Middle Term

15. 3. The middle tem must be distributed atleast once,
in the premises.
All lions are animals. Tu (+) Mp
All men are animals. tu (+) Mp
Thus, all men are lions. tu (+) Tp
* Fallacy of the Undistributed Middle Term
All trees are plants.
All kamagong are plants.
Thus, all kamagong are trees.

16. 4. If a term is distributed in the conclusion, then
such term must be distributed in the premise.
Some lawyers are holy. Tp (+) Mp
No criminals are holy. tu (-) Mu
Thus, no criminals are lawyers. tu (-) Tu
* Fallacy of the Illicit Major Term
All birds have wings. Mu (+) Tp
All birds are animals. Mu (+) tp
Thus, all animals have wings. tu (+) Tp
* Fallacy of the Illicit Minor Term

17. 5. There must be not 2 particular premises; one
premise atleast must be universal.
Some priest are holy. Tp (+) Mp
Some nuns are holy. tp (+) Mp
Thus, some nuns are priests. tp (+) Tp
*Fallacy of Two Particular Premises
Some scholars are wide-readers.
Some Filipinos are scholars.
Thus, Some Filipinos are wide-readers.

18. 6. If one premise is prticular, the conclusion must
be particular.
All lawyers are professionals. Tu (+) Mp
Some criminals are professionals. tp (+) Mp
Thus, some criminals are lawyers. tp (+) Tp
* Fallacy of Undistributed Middle Term
Some animals are two-legged.
All people are animals.
Thus, all people are two-legged.
* Fallacy of Universal Conclusion drawn from a
Particular Premise

19. 7. If the conclusion is negative, only one premise
must be negative.
No tenor is a soprano.
No soprano is a baritone.
Thus, no baritone is a tenor.
*Negative Premises
All lawyers are professionals.
Some criminals are not professionals.
Thus, some criminals are lawyers.
*Fallacy of Illicit Exclusion

20. 8. Two affirmative premises cannot give a negative
conclusion.
All stones are hard. Mu (+) Tp
Some diamonds are stones. tp (+) Mp
Thus, some diamonds are not hard. tp (-) Tu
* Fallacy of a Negative Conclusion drawn from
Affirmative Premises

21. 1. No heroes are cowards.
Some soldiers are cowards.
Thus, some soldiers are heroes.
2. All sacrifices are rewarding.
Some acts of cheating are rewarding.
Thus, all acts of cheating are sacrifices.
3. Some pilots are not happy-go-lucky.
All pilots are risk-takers.
Thus, some risk-takers are happy-go-lucky.
4. Some mosquitoes are blood-suckers.
All vampires are blood-suckers.
Thus, all vampires are mosquitoes

22.  Figure 1 (SUB-PRE)
 M T
t M
Thus, t T
1. The major premise must be universal.
2. The minor premise must be affirmative.

23.  The major premise must be universal.
 Some males are married.
All priests are males.
Thus, some priests are married.
 The minor premise must be affirmative.
 All surgeons are doctors.
No anesthesiologists are surgeons.
Thus, no anesthesiologists are doctors.

24.  BARBARA – AAA
 CELARENT – EAE
 DARII – AII
 FERIO - EIO

25.  Figure 2 (PRE-PRE)
 T M
t M
Thus, t T
1. One premise must be negative.
2. The major premise must be universal.

26.  One premise must be negative.
All great scientists are college graduates.
Some prof. athletes are college graduates.
Thus, some prof. athletes are great scientists.
 The major premise must be universal.
Some lawyers are liars.
No honest citizens are liars.
Thus, no honest citizens are lawyers.

27.  CESARE – EAE
 CAMESTRES – AEE
 FESTINO – EIO
 BAROCO - AOO

28.  Figure 3 (SUB-SUB)
 M T
M t
Thus, t T
1. The minor premise must be affirmative.
2. The conclusion must be particular.

29.  The minor premise must be affirmative.
All murdered are criminals.
No murderers are saints.
Thus, no saints are criminals.
 The conclusion must be particular.
Some movies are violent.
All movies are works of art.
Thus, all works of art are violent.

30.  DARAPTI – AAI
 DISAMIS – IAI
 DATISI – AII
 FELAPTON – EAO
 BOCARDO – OAO
 FERISON - EIO

31.  Figure 4 (PRE-SUB)
 T M
M t
Thus, t T
1. If the MP is affirmative, the mp must be
universal.
2. If the mp is affirmative, the conclusion must
be particular.
3. If one premise is (-), the MP must be
universal

32.  If the MP is affirmative, the mp must be
universal.
Some males are criminals.
Some criminals are females.
Thus, some females are males.
 If the mp is affirmative, the conclusion
must be particular.
All postmen are workers.
Some workers are professors.
Thus, all professors are postmen.

33.  If one premise is negative, the MP must be
universal.
Some criminals are terrorists.
No terrorists are women.
Thus, no women are criminals.

34.  BRAMANTIP – AAI
 CAMENES – AEE
 DIMARIS – IAI
 FESAPO – EAO
 FRESISON - EIO

35. 1. Is AOO a valid mood under figure 1?
2. Is OAO a valid mood under figure 2?
3. Is AEE a valid mood under figure 3?
4. Some politicians are pro-poor.
Some teachers are pro-poor.
Thus, some teachers are politicians.
5. All carabaos are black.
Some cats are black.
Thus, some cats are carabaos.

36.  Its major premise is a hypothetical proposition,
while its minor premise and conclusion are
categorical propositions. Here, there is no major
term (P), minor term (S), & middle term (M).
 If the students plagiarize, then they should be
punished.
The students plagiarize.
Therefore, they should be punished.

37. 1. Conditional Syllogism
MP – Hypothetical Proposition
mp – Categorical Proposition
C – Categorical Proposition

38. 1. Posit the antecedent, posit the consequent
(MODUS PONENS)
-If the antecedent is affirmed in the mp, the
consequent must also be affirmed in the conclusion.
Consequent’s truth follows from the antecedent’s.
Ex: If someone wins in the lotto draw, one becomes a
millionaire.
Son Gokou wins in the lotto draw.
Thus, Son Gokou becomes a millionaire.
*p‫כ‬q
p
‫؞‬q VALID

39. 2. Sublate the consequent, sublate the antecedent.
(MODUS TOLLENS)
- If the consequent is rejected in the mp, the
antecedent must also be rejected in the conclusion.
Antecedent’s falsity follows from the consequent’s.
Ex: If the best pres. cand. is Miguel Imburnal, then the
worst pres. cand. is Pepot Kuyukot.
The worst pres. cand. Is not Pepot Kuyukot.
Thus, the best pres. cand. is not Miguel Imburnal.
*p‫כ‬q
~q
‫~ ؞‬p VALID

40. 3. Posit the consequent, no conclusion (Fallacy of
Affirming the Consequent)
- Committed when the consequent is affirmed in the
mp.
Ex: If it is raining, then Rolando is absent.
Rolando is absent.
Thus, it is raining.
(There must be no conclusion)
*p‫כ‬q
q
‫؞‬p INVALID

41. 4. Sublate the antecedent, no conclusion (Fallacy of
Rejecting the Antecedent)
- It is committed when the antecedent is rejected in
the mp.
Ex: If it is raining, then Roland is absent.
It is not raining.
Thus, Roland is not absent.
(There must be no conclusion)
*p‫כ‬q
~p
‫~ ؞‬q INVALID

42. 1. If this month is December, next month is January.
This month is not December.
Thus, next month is not January.
2. If you failed in the test, you did not pass.
You did not pass.
Thus, you failed.
*EXEMPTIONS

43. Identify the proper conclusion to these c.syllogisms if the
mp is valid. If the mp is invalid, place NO CONCLUSION.
1. If you cheat, you will fail.
You did not cheat.
_________________________
2. If UST beats ADMU in this game, we will be exempted from the final
exam.
UST did not win in this game.
_________________________
3. If each O is P, then no R is S.
All R is S.
_________________________
4. If every B is C, then each D is I.
No D is I.
_________________________
5. If every B is C, then each D is I.
No B is C.
__________________________

44. MP – Disjunctive Proposition
mp – Categorical Proposition
C - Categorical Proposition
Ex: Jojo Kulot is either guilty or not guilty.
Jojo Kulot is guilty. (affirmed)
Thus, Jojo Kulot is not guilty. (rejected)

45. 1. Strict Disjunctive
- “Only one member is true & both cannot be true”
Ex: Either Angge is a truthful person or a liar.
She is telling the truth.
Thus, she is not a liar.
*p ˅ q
p
‫~ ؞‬q

46. *Strict Disjunctive follows the rule:
1. Posit one or more member of the MP in the mp, then
sublate the remaining in the conclusion.
(Ponendo-tollens)
*p ˅ q *p ˅ q
p or q
‫~ ؞‬q ‫~ ؞‬p
 The accused is either guilty or not guilty.
He is guilty.
Thus, he is not not guilty

47. 2. Sublate one or more member of the MP in the mp,
then posit the remaining in the conclusion.
(Tollendo-ponens)
*p ˅ q *p ˅ q
~p or ~q
‫؞‬q ‫؞‬p
 The military operation in Basilan is either successful
or unsuccessful.
It is not successful.
Thus, it is unsuccessful.

48. *Broad Disjunctive
- “Only one member is true, but both may also
be true.”
- Sublate 1 or more members of the MP in the
mp, then posit the remaining in the C.
Either Pepe likes to dive or play chess.
Pepe does not like to dive.
Thus, he likes to play chess.
*p ˅ q *p ˅ q
~p or ~q
‫؞‬q ‫؞‬p
 It is possible that he does not likes to do both.

49.  Pepe was not able to finish his thesis either because
he is lazy or deadened.
He is not lazy.
Thus, he is deadened.
*p ˅ q
~p
‫؞‬q
 Pepe was not able to finish his thesis either because
he is lazy or deadened.
He is lazy.
Thus, he is not deadened.
*p ˅ q
p
‫~ ؞‬q

50. MP – Conjunctive Proposition
mp – Categorical Proposition
C - Categorical Proposition
Rule 1: Posit one alternative, sublate the other.
Ex: You cannot be a good husband and philosopher at
the same time.
You are a good husband.
Thus, you are not a good philosopher.
* ~(p • q)
p
‫~ ؞‬q

51. Rule 2: Sublate one alternative, no conclusion
Ex: The passenger cannot be in the tricycle and in the
bus at the same time.
He is not in the tricycle.
Thus, he is in the bus.
* ~(p • q)
~p
‫ ؞‬q

52. 1. (p ‫ כ‬q) ‫ כ‬r
~q
‫(~ ؞‬p ‫ כ‬r)
2. (p ‫ כ‬q) ˅ (q ˅ r)
~(q ˅ r)
‫؞‬p‫כ‬q
3. (p ‫ כ‬q) • r
p‫כ‬q
‫~ ؞‬r
4. If Angola achieves stability, then both Botswana
and Chile will adopt more liberal policies. But
Botswana will not adopt a more liberal policy. Thus,
Angola will achieve stability.

53. 1. If Montana suffers a severe drought, then, if
Nevada has its normal light rainfall, Oregon’s
water supply will be greatly reduced. Nevada
does have its normal light rainfall. So if Oregon’s
water supply is greatly reduced, then Montana
suffers a severe drought.
2. p ‫( כ‬q • r)
(q ˅ r) ‫ כ‬s
‫؞‬p‫כ‬s