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#### • inductive and deductive reasoning in geometry

Question:1. By observing many individual cases, people concluded that breathing air in swampy areas cause malaria. 2. Any quadrilateral with four equal sides is a rhombus. Figure ABCD has four congruent sides. therefore figure ABCD is a rhombus. (there is no figure) please give a brief description on what u did. or not

Answers:1. Inductive. You're looking for the cause. You already know the effect. Inductive reasoning is the reverse of deductive reasoning. You go backwards. 2. Deductive. You establish a premise that is known to be true, make a statement that fits the premise, then draw a conclusion from the premise.

Question:I am going over practice test problems in my textbook for a test tomorrow. I am stuck on this one and want to make sure I get it. Which of the following is an example of inductive reasoning? a. Ashley measures the angles of several triangles and finds that their measures all add up to 180. She conjectures that the sum of the measures of the angles in any triangle is always 180. b. Ashley knows that the sum of the measures of the angles in a square is always 360. She conjectures that if she draws a square, the sum of the measures of the angles will be 360. c. Ashley learns that the measures of all acute angles are less than 90. She conjectures that if she sees an acute angle, its measure will be less than 90. d. Ashley reads in her textbook that the measures of all right angles is 90. She conjectures that the measure of each right angle in a square equals 90.

Answers:Inductive Reasoning: A type of mathematical reasoning which involves observing patterns and using those observations to make generalizations. I would say the answer is A. Because she is actually doing the measuring and observing that similar pattern, and then making a mathematical generalization based on her results; instead of just "knowing", "learning", or "reading".

Question:It has said that deductive argument are attempt to show that a conclusion necessarily follows from a set of premises or hypotheses. A deductive argument is valid if the conclusion does follow necessarily from the premises. If so, should all deductive argument are valid? According to the definitions above, they are the same thing, right? Then why there are deductive argument that are invalid? Can you give me some examples? Thanks.

Answers:The answer to your question is largely dependent on the definition of "deductive argument". Some popular logic textbooks treat deductive argument and inductive argument as basic concepts of logic. This seemingly minor difference marks a big difference in regard to the treatment of basic concepts of logic. The terms valid and invalid can quite easily be defined independently of the term deductive argument. Similarly, the terms strong and weak can be defined independently of the term inductive argument. But in some widely used logic textbooks, valid and invalid are defined in terms of deductive argument ; strong and weak are defined in terms of inductive argument. Why would anyone regard the concepts of deductive argument and inductive argument as more basic than the concepts of validity and strength? The idea is that we can neatly sort arguments into two major groups (deductive and inductive), and that the concepts of validity and invalidity apply only to deductive arguments, while the concepts of strength and weakness apply only to inductive arguments. Deduction is about deductive arguments; induction is about inductive arguments. Thus, we seem to get a nice, simple picture of the whole of logic. But in the end, an invalid argument is really not deductive. It may have some sort of form that with only minor adjustments could be made into a valid argument, and this is why some textbooks treat it this way.

Question:another question i got is: Compare and contrast the reasoning proceses of inductive vs. deductive reasoning. use examples to support your comparisons?