Answer:
e. HS
Step-by-step explanation:
The argument:
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
is an instance of one of hypothetical syllogism (HS).
Hypothetical syllogism contains conditional statements for its premises.
Let
p = [(P ≡ T) • (H • N)]
q = (T ⊃ ~S)
r = [(H ∨ E) ∨ R]
The this can be interpreted as:
p ⊃ q
q ⊃ r
p ⊃ r
This interprets that:
If p then q
but if q then r
therefore if p then r
Thus, in logic HS is a valid argument form:
p → q
q → r
∴ p → r
Note that ⊃ symbol is used to symbolize implication relationships. This is used in conditional statements which are represented in the if...then... form. For example p ⊃ q means: if p then q. So the type of Hypothetical syllogism used in this is conditional syllogism.
There are three parts of syllogism:
major premise
minor premise
conclusion
An example is:
If ABC is hardworking, then ABC will go to a good college.
Major premise: ABC is hardworking.
Minor premise: Because ABC is hardworking , ABC will score well.
Conclusion: ABC will go to a good college.
Example of Hypothetical syllogism:
If AB is a CD, then EF is a GH
if WX is a YZ, then AB is a CD
therefore if WX is a YZ, then EF is a GH
This can be understood with the help of an example:
If you study the topic, then you will understand the topic.
If you understand the topic, then you will pass the quiz.
Therefore, if you study the topic, then you will pass the quiz.
