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. Â
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. Â
If you understand the topic, then you will pass the quiz.
Therefore, if you study the topic, then you will pass the quiz.
