HPSlec92010 - Lecture # 9 Informal Review of Systems of...

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Lecture # 9 Informal Review of Systems of Logic AGENDA I. Logic Brain Teasers for Thursday II. Boolean Logic III. Other Logics A. First Order Predicate Logic B. Second Order predicate Logic There will not be any lecture study questions on the various types of logic that I describe in this lecture, but there will be some on the brain teasers-- but after the midterm.
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I. Logic Brain Teasers for Thursday AGENDA Here is a set of famous problems involving logical reasoning. Some involve imagery in reasoning. Try your hand on them. They will come next Tuesday. Please spend some time thinking about them. Several are not easy, so don’t despair if the solution doesn’t come. I have numbered the problems
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1. Imagery and Deductive Reasoning Brain Teasers After years of ‘behavioristic, S-R blackout’ for any reference to mental processes, cognitive scientists have begun to accept that imagery plays a role in reasoning. Lets consider a simple problem: I have a cube cut neatly into 27 equal cubes by three slices on top and the sides: Oops-Sorry! Think of It as neater.
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The Cube Problem Now the top and bottom of the cube are painted green and the four sides are painted blue . You must not write anything! How many little cubes have at least one green and at least one blue side? It is hard to imaging solving this without using imagery.
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2. A Famous problem that Gave Computer Scientists Nightmares. You have an 8” by 8” array of equal size 1” by 1” little squares. You have a large box of 2” by 1” dominos
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Two Tiling Problems Problem #IIa. (Very easy). Can you ‘tile’ the 8” by 8” array with 2” by 1” dominos? By tile I mean cover each of the 64 squares with no overlaps and no dominos hanging off the array? Problem #IIb. ( Very Hard). Suppose I snip of the lower left and upper right squares. Now 62 squares are left. Can I tile the array with the two squares missing? Two Hints: The problem follows the imagery problem, and I mentioned earlier that I am a chess master.
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3. A Brain Teaser Involving our Friend- The Bookworm #1.Lets go back to the 27 little cubes, but do not worry about how we colored it in the earlier problem. We have a little cube-eating-worm! Our worm devours the top-left-front cube and continues to eat all the little cubes. Once he eats a cube he must pick the next cube as an adjacent one with a shared wall- up, down left-right, lower-upper. Can the worm save the middle most cube to be the last one eaten? Start Top of cube This is a hard problem!- but you do have a hint in why I am giving it after the last problem. Worm has three choices for next Feast- the two checks and the one below start
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4. A Mixture Brain Teaser I have two quart beakers, A with a pint of coffee and B with a pint of cream. I take a tablespoon of the coffee and pour it into B, mix it
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HPSlec92010 - Lecture # 9 Informal Review of Systems of...

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