# + A - B

```Hypothetical
Syllogism
Hypothetical syllogism
-a deductive argument which asserts
the sequential relation between the
two elements of a hypothetical
proposition
-its main premise is a hypothetical
proposition
Analysis of a hypothetical prop.
If it rains, then the roof is wet
A-antecedent
+A
+C
+C
?A
C-consequent
-C
-A
-A
?C
Example
If public officials committed serious
lapses, then they will be charged
Some police officers committed serious
lapses.
+A
Valid
Hence, they will be charged
+C
Joe will not comeback unless he loves
Michelle
-C
Joe will come back
Valid
Ergo, he loves Michelle - A
If you truly love a person, you don’t stifle
her growth.
Mickey lets go of Minnie to give her
space for growth.
+C Invalid
+A
Thus, Mickey truly loves Minnie
Types of Hypothetical Syll.
Conditional
Simple Conditional
If… then…
Unless…
Reciprocal Conditional
Only if C, A
Types of Hypothetical Syll.
Conditional
Biconditional
If and only if…
Pure conditional
If B, then C
If A, then B
Ergo, if A, then C.
Reciprocal conditional
Only if students are treated as mature
persons will they act responsibly
But students are treated as mature
+C Invalid
persons.
Hence, they will act responsibly.
+A
Biconditional
If and only if Perf is a millionaire will Cath
marry him
Perf is not a millionaire
-A Valid
Hence, Cath will not marry him.- C
+A + C - C
+C + A - A
-A
-C
Pure conditional
If A is B, then _________
X is Y.
Common Element
If _________
X is Y, then C is D.
Ergo, if A is B, then C is D.
Rule:
The common element must be used once as antecedent
and consequent.
If Nolan is honest, then he will tell the truth. If he will tell
the truth, then he will implicate the officials behind illegal
gambling.
Thus, if Nolan is honest, then he will implicate the
officials behind illegal gambling.
Pure conditional
If the president is sincere in stopping corruptions, she
will investigate the COMELEC.
If she will investigate the COMELEC, she will discover the
anomalous transactions on election automation.
Hence, if the president is sincere in stopping corruptions,
she will discover the anomalous transactions on election
automation.
If Filipinos live a truly Christian life, then they will take
care of their environment. If Filipinos show true concerns
for the environment, then they will take care of their
environment. Thus, if Filipinos show true concerns for
the environment, then they live a truly Christian life.
Disjunctive Syllogism
-a type of hypothetical syllogism whose main
premise is a disjunctive proposition (Either…
or…)
Types of Disjunctive
a) Perfect Disjunctive
-the main premise contains alternatives that
cannot be both affirmed and denied.
Either he
is telling the truth or _____________
he is telling a lie.
________________
+A
-B
-A
+B
+B
-A
-B
+A
Perfect Disjunctive
Matt is either a theist or an non-theist.
-B
He is not a non-theist.
Valid
+A
Therefore, he is a theist.
Jie’s necklace is either rare or common.
Jie says it is rare.
+A
Valid
Hence, it is not common - B
Disjunctive Syllogism
Types of Disjunctive
a) Imperfect Disjunctive
-the main premise contains alternatives that
cannot be both denied but can be both
affirmed
Either_______
you try or you
won’t succeed.
______________
+A
?B
-A
+B
+B
?A
-B
+A
Imperfect Disjunctive
Singapore.
He is not going to Singapore. -B
Valid
Either he will engage in business or he will
continue being an employee.
Georg will engage in business. + A
So, he will not continue being an - B
Invalid
employee.
Conjunctive Syllogism
-a type of hypothetical syllogism whose main
premise is a conjunctive proposition (cannot
be both… and…)
-the main premise contains alternatives that
cannot be both affirmed but can be both
denied.
Pierre cannot be both in
Albay and in
Alcoy atst.
______
________
+A
-B
-A
?B
+B
-A
-B
?A
Conjunctive Syllogism
Fred cannot both be a civil servant and a
private businessman at the same time.
He is not a civil servant at this time -A
Invalid
+B
So, he is a private businessman.
No government prosecutor can both
vigorously do his job and receive bribe at the
same time.
Some state prosecutors are not doing their
-A
jobs vigorously.
Invalid
Thus, they are receiving bribes.+ B
The accused is either innocent or guilty.
+A
Guevarra claims he is innocent.
Valid
Hence, he is guilty.Perfect Disjunctive- B
Either the president will not support population
control program or Church groups will criticize
him.
Imperfect Disjunctive
Many pro-Life Church groups are criticizing the
+A
president.
Invalid
So, he is supporting population control. - B
One cannot be both a Muslim and Christian
altogether. Conjunctive
Invalid
Derek is not a Muslim. - A
+B
So, he is a Christian.
```