2.2 inductive and deductive reasoning. what we will learn use inductive reasoning use deductive...

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2.2 Inductive and Deductive Reasoning

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Page 1: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

2.2 Inductive and Deductive Reasoning

Page 2: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

What We Will Learn

Use inductive reasoningUse deductive reasoning

Page 3: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Needed Vocab.

Conjecture: an unproven statement that is based on observations

Inductive reasoning: find a pattern and write a conjecture

Counterexample: specific case for which the conjecture is false

Deductive reasoning: uses facts, definitions, accepted properties, and laws of logic to form a logical argument

Law of Detachment: if the hypothesis of a true conditional is true, then the conclusion is true

Law of syllogism: If hypothesis p, then conclusion q and if hypothesis q and conclusion r. Therefore; if hypothesis p, then conclusion r.

Page 4: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Ex. 1 Writing Conjectures

Write the conjecture and write next two terms.

1, -2, 3, -4, 5,… Alternating negative and going up by 1 -6, 7

z, y, w, x, v,… Alphabet backwards u, t

o, t, t, f, f, s, s,… First letter of numbers e, n

Page 5: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Ex. 2 Making and Testing a Conjecture

the sum of any three consecutive integers.Do a couple of examples to find pattern and

then write conjecture using phrase 10+11+12 = 33 20+21+22 = 63 5+6+7 = 18 8+9+10 = 27

pattern: answer is three times middle number Conjecture: The sum of any three consecutive integers

is three times the middle number. Then test conjecture for accuracy

• If wrong, rethink conjecture

Page 6: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Your Practice

The product of any two even integers.2*4 = 8 4*6= 242*10 = 20 6*8 = 48

pattern: answers is positiveConjecture: The product of any two even

integers is a positive answer.Test: 6*20 = 120

Page 7: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Ex. 3 Finding a Counterexample

The sum of two numbers is always more than the greater number. Find counterexample if one. Only need one

-2 + (-4) = -6

The value of x2 is always greater than the value of x. (0)2 = 0

If two angles are supplements of each other, then one of the angles must be acute. Right angles

Page 8: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Ex. 4 Law of Detachment

Must be told hypothesis is true.If two segments have the same length, then

they are congruent. You know that BC = XY. What can you conclude? Are you told hypothesis is true?

BC XY

If you pass the final exam, then you pass the class. You pass the final exam.

What can you conclude? Are you told hypothesis is true?

You pass the class

Page 9: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Your Practice

If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles.

Hypothesis is not told true, so cannot make a conclusion

Page 10: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Ex. 5 Law of Syllogism

If hypothesis p, then conclusion q. If hypothesis q, then conclusion r. If conclusion of one is hypothesis of other, then use law

of syllogismSyllogism say: If hypothesis p, then conclusion r.If a polygon is regular, then all angles in the

interior of the polygon are congruent. If all the angles in the interior of a polygon are congruent, then the sides of the polygon are congruent. If a polygon is regular, then the sides of the polygon are

congruent.

Page 11: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Your Practice

If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel.

If a figure is a rhombus, then the figure has two pairs of opposite sides that are parallel.

Page 12: 2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning

Ex. 7 Inductive or Deductive

Inductive based on patterns.Deductive based on definitions and

properties.Each time Monica kicks a ball into the air, it

returns to the ground. Next time Monica kicks a ball up in the air, it will return to the ground. Which is it?

Inductive because observable pattern