The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form. [(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]

a. MP
b. DS
c. MT
d. Conj
e. HS

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.

y = x + 95

y = 42 + 95

y=137 mm hg

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: