Question

For propositional calculus, I have a HW assignment out of the textbook Applied Discrete Structures by Alan Doerr and Kenneth Levasseur. I'm having a hard time figuring which statements should be propositions and what arguments imply which.

Here's the problem is question:

6. Determine the validity of the following argument: For students to do well in a discrete mathematics course, it is necessary that they study hard. Students who do well in courses do not skip classes. Students who study hard do well in courses. Therefore students who do well in a discrete mathematics course do not skip class.

So far this is what I have (but I'm not sure if it's correct):

Let a be the proposition, "Students do well in a discrete mathematics course."

Let b be the proposition, "It is necessary to study hard."

Let c be the proposition, "Students do not skip class."

Let d be the proposition, "Students who study hard."

So that would make my arguments:

a -> b

c

d

=> a -> c

Is this correct?

Thank you!

Answer 1

plz feel free to comment in case of doubts as i am happy to help you. Plz do like and upvote the solution if u r satisfied. Thanks..

"a = ""students do well in discrete math course"" b = "" it is necessary to study hard"" c = "" students do not skip classes"" d = "" students do well in courses "" given that, a rightarrow b (1 st sentence) d rightarrow c (2 nd sentence) b rightarrow d (3 rd sentence) (b rightarrow d) and (d rightarrow c) implies b rightarrow c Again (a rightarrow b) and (b rightarrow c) implies a rightarrow c i.e students do well in discrete math course rightarrow they don't skip class Hence, the argument (a rightarrow c) is valid"