Related questions with answers

[Related to Solved Problem 2.1on page 44] You have exams in economics and chemistry coming up, and you have 5 hours available for studying. The following table shows the trade-offs you face in allocating the time you will spend studying each subject:

Hours Spent Studying	Hours Spent Studying	Hours Spent Studying	Midterm score	Midterm score
Choice	Economics	Chemistry	Economics	Chemistry
A	5	0	95	70
B	4	1	93	78
C	3	2	90	84
D	2	3	86	88
E	1	4	81	90
F	0	5	75	91

Label the points representing choice C and choice D. If you are at choice C, what is your opportunity cost of increasing your chemistry score by 4 points?

Is water freezing a chemical or physical change?

Each boldface number is the value of either a parameter or a statistic. In each case, state which it is. In an experiment to test the effectiveness of single -sex classrooms, girls assigned at random to a coeducational chemistry class gained an average of 12.2 points from a pretest to a posttest. Girls assigned randomly to a single-sex chemistry class taught by the same teacher gained 15.1 points.

Question

Determine whether each statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. (1) If it is Tuesday, then Marla tutors chemistry. (2) If Marla tutors chemistry, then she arrives home at 4 P.M. (3) If Marla arrives home at 4 P.M., then it is Tuesday.

Solution

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Step 1

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Law of Detachment states if $p\Rightarrow q$ is true and $p$ is true, then $q$ is true. Law of Syllogism states if $p\Rightarrow q$ and $q\Rightarrow r$ are true, then $p\Rightarrow r$ is true.

Notice that Statement (3) is an If-then statement which means Law of Detachment can't be used since the conclusion of Law of Detachment is not an If-then statement.

For Statement (1), $p$ is it is Tuesday" and $q$ is Marla tutors chemistry". For Statement (2), $q$ is Marla tutors chemistry" and $r$ is she arrives home at 4 P.M." The conclusion using Law of Syllogism would then be the statement ``If it is Tuesday, then Marla arrives home at 4 P.M." Statement (3) is the converse of this conclusion so the statement is invalid.