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Deductive Reasoning

Deductive Reasoning. Honors Geometry Chapter 2, Section 4. In Preparation . Open your browsers to maps.google.com Type in Dublin select Dublin, Ireland from the drop down Menu Click the satellite button on the top right of the map portion of the page.

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Deductive Reasoning

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  1. Deductive Reasoning Honors Geometry Chapter 2, Section 4

  2. In Preparation • Open your browsers to maps.google.com • Type in Dublin • select Dublin, Ireland from the drop down Menu • Click the satellite button on the top right of the map portion of the page. • Repeat the same procedure for Beijing, China and Cairo, Egypt • Close your laptop

  3. Notes • Deductive Reasoning: uses facts, definitions, and true statements whether assumed or proved to come to conclusions. • Law of Detachment: says that if an if-then statement is true and its hypothesis is true, then its conclusion must also be true. • If p q is true and p is true then q is true • Example: • True Statement: If you over mix your biscuit dough, then it will not rise. • From the law of detachment, I can be assured that my biscuits will be flat and hard if I over mix the dough.

  4. On your own: Use the law of detachment to come up with a conclusion • Open laptops • If I visit Germany, then I’ll have to learn to eat sour kraut. • I’m visiting Prague this summer. • Is the hypothesis satisfied? Is it true? What can you conclude?__________________________ • What if I visit Frankfurt? _____________________ • If I have to learn to eat sour kraut, does that mean I’m going to Germany?__________________ • Confirmation of the conclusion doesn’t ensure that the hypothesis is true. • The point: the hypothesis must be true for the conclusion to be true • Close laptops

  5. Notes • Law of Syllogism: says • If p q is true and q r is true, then p r is true also • It’s like a road that gets you to your destination • Example: • True Statement 1: If I get into the pool, then I have to shower first. • True Statement 2: If I have to shower first, then I will be cold before I’m even in the water. • It is horrible rushing to the pool after taking that cold shower isn’t it!

  6. On your own: Use the law of syllogism to answer this question • Open laptops • Statements • If I want to fly to Hamburg, then I have to stop in either London or Munich • If I stop in Munich, I must see Neuschwanstein. I have always wanted to see the most famous of Europe’s castles. • On my way to Hamburg this spring, will I get my wish to see Neuschwanstein? _______________________ • Was there a link between one if-then statement and the next? • _________________________ • How could I have rephrased the second statement to make it so a conclusion could be reached? • _________________________________ • The Point: There has to be a link between the two statements, and you have to proceed from hypothesis to conclusion in your reasoning. • Close laptops

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