Conjecture: Carlos is in Antarctica. Hypothesis: Conclusion: The conjecture is b. Given: If a person sees a polar bear, then the person is in the Arctic. James is in the Arctic. Conjecture: James sees a polar bear. Hypothesis: Conclusion: The conjecture is The Law of Syllogism states that if p → q and q → r are true statements, then p → r is a true statement. p: You are a clown. q: You wear big shoes. r: Your feet hurt. Use the Law of Syllogism to complete a valid conjecture. Given: If you are a clown, then you wear big shoes. If you wear big shoes, then your feet hurt. Conjecture: If you are a clown, then ___________________.
Name Tell whether each conclusion is a result of inductive or deductive reasoning.a. The United States Census Bureau collects data on the earnings of American citizens.Using data for the three years from 2001 to 2003, the bureau concluded that the nationalaverage median income for a four-person family was $43,527.b. A speeding ticket costs $40 plus $5 per mi/h over the speed limit. Lynne mentionsto Frank that she was given a ticket for $75. Frank concludes that Lynne was driving7 mi/h over the speed limit.Determine if each conjecture is valid by the Law of Detachment.a. Given: You will catch a catfish if you use stink bait. Stuart caught a catfish.Conjecture: Stuart used stink bait. b. Given: An obtuse triangle has two acute angles. Triangle ABC is obtuse.Conjecture: Triangle ABC has two acute angles.Determine if each conjecture is valid by the Law of Syllogism.6. Given: If the gossip said it, then it must be true. If it is true, then somebody is in big trouble.Conjecture: Somebody is in big trouble because the gossip said it. _____________________7. Given: No human is immortal. Fido the dog is not human.
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