An expanded high school logic unit
Hey you wanna be a total pal and outline (as briefly as you need to) how you handle a logic unit? It’s the end of the year and I’ve been kind of bouncing around between argument and vocabulary without an exit strategy. Any help would be great.
Sure, and you (or anyone else), feel free to ask me to expand on my sometimes cryptic shorthand. What you do depends on how far you want to go, and in what direction.
(the good stuff’s beneath the fold –>)
- symbolize statements (not objects)
- and, or, if… then…
- logical equivalence (aka biconditional); operation or relation?
- truth tables (intro, for each operation)
- more complicated truth tables (and more complicated, etc)
- using truth tables to show logical equivalence: material implication
- Venn diagrams (demorgans laws)
- Euler diagrams (conditional and contrapositive; converse and inverse)
- Rules of inference: (these go by various names, so I will list them by what they do)
- p -> q; p : q
- p -> q; ~q: ~p
- p v q; ~p: q
- p -> q; q -> r: p -> r
- p; q: p & q
- p: p v q
- p&q: p
- Deductive proofs (symbolized, and from English)
- Indirect proofs
- Testing for validity
(I do a bit more, those are the most of the biggies)
I don’t handle all of these in exactly this way. You could pick your way through what’s interesting. You might want a whole lot of translation from whole language stuff (negation of English statements is tricky). Or you might want to get to Venn Diagrams or Euler Diagrams or Truth Tables, and just stop there and up the level of challenge. (Kids like that place). Or you might race to the rules of inference, and give them things like:
Jack likes Jill. Jill likes Steven or Jill likes Jack. Candy likes Bob and Jack. It is not true that Steven likes Candy and Jill. If Steven doesn’t like Candy, then Candy doesn’t like Bob. Jill likes Steven or Steven likes Jill. What are the chances of Jack and Jill hooking up?
I’ve done different things at different times. These days, with the luxury of a full term course, and 5 three-day weeks for this unit, and having already well-established what validity is in whole language context, I race through the start, hit tables and both sorts of diagrams, and get to proofs kind of fast, dwelling on both direct and indirect, as well as validity testing.