Daily Prep 2.4 -- MTH 225

--- tags: mth225, dailyprep --- # Daily Prep 2.4 -- MTH 225 ## Overview Our final topic in Module 2 (Logic) deals with **predicates** --- a statement that contains a variable, and different values of the variable lead to different truth outcomes. Predicates are important tools for our upcoming work on sets (Module 3) and recursion and induction (Module 5). You'll learn how to evaluate predicates and how to *quantify* and *negate* predicates. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. * Explain the differences between a predicate and a proposition. * Evaluate the truth value of a given predicate for different values of the input variable(s). * Determine the truth value of existentially and universally quantified predicates, and determine if a predicate is underdetermined. * Identify the correct negation of a quantified predicate. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. * Determine the domain and truth set of a predicate. * Determine the truth value of a double-quantified predicate. * Given a predicate: * Determine its truth set * Determine whether the predicate is true when universally quantified * Determine whether the predicate is true when existentially quantified * Write the negation * If the predicate has two variables, determine truth values for different combinations of quantification ## Resources for learning **Video:** Watch these from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 29:29): <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/598881354?badge=0&autopause=0&player_id=0&app_id=58479&h=33c858ee70" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 2.8: Predicates"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/600466128?badge=0&autopause=0&player_id=0&app_id=58479&h=2a59394446" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 2.9: Quantification"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/600490216?badge=0&autopause=0&player_id=0&app_id=58479&h=74ce90b919" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 2.10: Negating quantified statements"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> <iframe src="https://player.vimeo.com/video/602710401?h=2685a75e15" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe> <p><a href="https://vimeo.com/602710401">Screencast 2.11: Quantifying predicates with two variables</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p> **Text:** In the textbook, [read in Section 3.1](http://discrete.openmathbooks.org/dmoi3/sec_propositional.html) starting at the section "Beyond Propositions". You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. ## Exercises Once you have watched the videos above, go to this form and complete all the non-optional items on it: https://docs.google.com/forms/d/e/1FAIpQLSeSoYC6DDlcVyplSSE9WB1uqe1m0I4NixMk_hAwZSMy75-0YQ/viewform ## Submission and grading **Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully. **How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you: - Turn the work in before its deadline; - Leave no item blank or skipped, even accidentally; and - Give a good-faith effort at a correct answer on every non-optional item. More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document. When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.