Daily Prep 2.2 -- MTH 225

--- tags: mth225, dailyprep --- # Daily Prep 2.2 -- MTH 225 ## Overview How do you know when a logical proposition, especially a complicated one, is true and when it's false? And how can you tell if two statements that look different are actually "the same" from a logical standpoint? We'll answer these questions in this lesson with the concept of a **truth table**. Truth tables will allow us to answer the question of when two superficially different statements are **logically equivalent**. ## 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. - Give the truth tables for a basic conjunction, disjunction, negation, and conditional statement. - Construct a truth table for a proposition with only two atomic statements, and only one or two intermediate steps. - Determine if two propositions with two input statements are or are not logically equivalent by using a truth table. **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. - Construct truth tables for two-variable statements that have several intermediate steps. - Construct truth tables for three- and four-variable statements. - Use a truth table to determine whether two propositions (possibly complex ones) are or are not logically equivalent. ## Resources for learning **Video:** Watch these from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 14:38): <iframe title="vimeo-player" src="https://player.vimeo.com/video/592797708?h=7fabfc2432" width="640" height="360" frameborder="0" allowfullscreen></iframe> <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/593393012?badge=0&autopause=0&player_id=0&app_id=58479&h=ad4ea15742" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 2.6: Truth tables with intermediate steps"></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/597356440?badge=0&autopause=0&player_id=0&app_id=58479&h=d373ef30bf" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 2.7: More complex truth tables"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> **Text:** Nothing from the text this time. 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/1FAIpQLSfhbN0VFO22G6TsLv484AG_zpmbBsT4GeGVWpH0gVS5O4aYYQ/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.