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Valid and Invalid Arguments

Valid and Invalid Arguments. Section 1.6. Arguments. If a number is divisible by 8, then it is divisible by 4. 61 is not divisible by 4. 61 is not divisible by 8. Therefore symbol. Conclusion. Premises.

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Valid and Invalid Arguments

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  1. Valid and Invalid Arguments Section 1.6

  2. Arguments • If a number is divisible by 8, then it is divisible by 4. • 61 is not divisible by 4. • 61 is not divisible by 8. Therefore symbol Conclusion Premises

  3. **The validity of an argument is determined by the logical form, not by whether the conclusion is true or false. • There are three valid forms that we will learn about today: • Law of Detachment • Law of Transitivity • Law of Indirect Reasoning

  4. Law of Detachment • If P then Q • P • Q • Example: Notice how P is Detached from Q

  5. Law of Transitivity • If p then q • If q then r • if p then r • Example: If Jamie gets an animal, she will get a dog. • If Jamie gets a dog, it will be a poodle. • If Jamie gets an animal, she will get a poodle. Remember the transitive property Of equality? A = B, B = C, so A = C

  6. Law of Indirect Reasoning • If p then q • Not q • not p • Example: • If it is sunny, I will wear sunglasses. • I did not wear sunglasses. • It was not sunny.

  7. Which type of reasoning is this?What conclusion can be determine? • If the moonflowers are blooming, then it is nighttime. It is daytime. • If a polygon is regular, all its sides are congruent. The sides of P are not all congruent. • If it’s Sunday, then Teri reads the comics. Teri reads the comics. Law of Detachment; the moonflowers are not blooming. Law of Indirect Reasoning; The polygon is not regular.

  8. Warning!!! They will try to Trick you!!!

  9. If it’s Sunday, then Teri reads the comics. Teri reads the comics. • P  Q • Q • P? • This is called a converse error, making the statement invalid.

  10. Another Invalid form.. Inverse Error • If we go to the movies, we will see an action movie. • We did not go to the movies. • We did not see an action movie. p  q ~p ~q ?

  11. Last Invalid Form… • On July 1st, it rained. • On July 2nd, it rained. • On July 3rd, it rained. • it rains the entire month of July. • This is called “improper induction”  you are jumping to a conclusion!

  12. Homework Page 51 – 54 2- 28 (evens)

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