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DG Unit 2
Vocab Chapter 2 Discoverying Geometry
| Question | Answer |
|---|---|
| The process of observing data, recognizing patterns and making a generalization | Inductive Reasoning |
| a educated guess | Conjecture |
| an example that shows a conjecture is false | Counterexample |
| the process of showing that certain statements follow logically from agreed upon assumptions and proven facts | Deductive Reasoning |
| a argument that follows either the Law of Detachment, Law of Contrapositive or Law of Syllogism | Valid Argument |
| a statement written in If______then_______form. | Conditional Statement |
| a sequence of numbers where the difference between consecutive numbers is constant | Arithmetic Sequence |
| a sequence of numbers where the ratio between consecutive numbers is constant | Deductive Sequence |
| A____________definition describes a sequence whose terms are defined by one or more preceding terms. Known terms are used to calculate new terms | Recursive |
| A ____________definition describes a sequence using the begining term and either a common difference or ratio. This definition is used to calculate any term in a sequence. | Explicit |
| a statment formed by switching the hypothesis and conclusion of a conditional statement | Converse |
| a statement formed by negating the hypothesis and conclusion of a conditional statement | Inverse |
| a statement formed by switching and negating the hypothesis and conclusion of a conditional statement | Contrapositive |
| a statement formed by combining a conditional statement and its converse when both are true. | Biconditional |
| The ______________is logically equal to the orginal | Contrapositive |
| The _____________is logically equal to the inverse | converse |
| What is the converse: " If Snoopy is wearing a scarf and goggles, then he is going to fight the Red Baron | If Snoopy is going to fight the Red Baron, then he is wearing a scarf and goggles. |
| What is the inverse: "If an angle greater than 90 degrees, then it is an obtuse angle" | If an angle is not greater than 90 degrees then it is not obtuse. |
| What is the contrapositive: "If the Cards win their division, then they will go to the playoffs" | If the Cards did not go to the playsoff, then they did not win their division. |
| Valid or Invalid? If valid what law of deduction. Premise 1: If Paul is tall then Paul plays volleyballPremise 2: Paul is tallConclusion: Therefore Paul plays volleyball | Valid, Law of Detachment |
| Valid or Invalid? If valid what law of deduction. Premise 1: If Paul is tall then Paul plays volleyballPremise 2: Paul plays volleyball Conclusion: Therefore Paul is tall | Invalid |
| Name the three laws of deduction | Law of DetachmentLaw of Contrapositive Law of Syllogism |
| Valid or Invalid? If valid what law of deduction. Premise 1: All accountants use math in their work.Premis 2: Beth is an accountant.Conclusion: Therefore, Beth uses math in her work | Valid, Law of Detachment |
| Valid or Invalid? If valid what law of deduction. Premise 1: All accountants use math in their work.Premise 2: Beth does not use math in her work Conclusion: Therefore, Beth is not an accountant | Valid, Law of Contrapositive |
| Valid or Invalid? If valid what law of deduction. Premise 1: All accountants use math in their work.Premise 2: Beth is not an accountant Conclusion: Therefore, Beth does not use math in her work | Invalid. |
| Valid or Invalid. If valid identify the law of deductive used. Premise 1: If you live in Phoenix then you live in AZPremise 2: If you live in AZ, then you live in then U.S.AConclusion: Therefore, If you live in Phoenix then you live in the USAfollo | Valid Law of Syllogism |
| Write a biconditional statement using the 90 degrees. | An angle is a right angle if and only if it measures 90 degrees. |
| Fill in the conclusion.Premise 1 All Math II students are brillant.Premise 2 Joe is not brillant Conclusion_________________________ | Joe is not a Math II student |
| Fill in the conclusion.Premise 1 All Math II students are brillant.Premise 2 Joe is a Math II studentConclusion_________________________ | Joe is brillant |
| What was the original conditional statement if its inverse was "If you cannot see the Sun in the ski, then it is not daytime | If you can see the Sun in the sky, then it is daytime. |
| What was the original conditional statement if its converse was "If I am one the 3rd planet from the sun, then I am on Earth" | If I am on Earth, then I am on the third planet from the sun. |
| What is the original statement if the contrapositive was "If a polygon is not a pentagon, then it does not have 5 sides. | If a polygon has 5 sides, then it is a pentagon. |
| Fill in the conclusionPremise 1: If Rays buys a new TV, the he can watch two games at one. Premise 2: If Ray can watch two games at once, then his girlfriend will break up with him. Conclusion___________________________________ | If Ray buys a new TV then his girlfriend will break up with him. |
| What is the converse of the statement?"If a triangle is isosceles, then it has two equal sides" | If a triangle has two equal sides, then it is isosceles. |
| What is the inverse of the statement?"If a triangle is isosceles, then it has two equal sides" | If a triangle is not isosceles then it does not have two equal sides. |
| What is the contrapositive of the statement?"If a triangle is isosceles, then it has two equal sides" | If a triangle does not have two equal sides, then it is not isosceles. |
| Premise 1:If P then Q Premise 2:not Q Therefore: not P demonstrates which Law of Deductive Reasoning, | Law of Contrapositive |
| Premise 1:If P then Q Premise 2:PTherefore: Q demonstrates which Law of Deductive Reasoning, | Law of Detachment |
| Premise 1: If P then Q Premise 2: If Q then RConclusion: If P then R | Law of Syllogism |
| Use the Law of Detachment to fill in the missing premise. Premise 1: All___________are _____________Premise 2: Snoopy is a dogConclusion: Snoopy is a mammal | All dogs are mammamls |
| Use the Law of Contrapositive to fill in the missing premise. Premise 1: All_dogs are mammals Premise 2: Snoopy is________________________Conclusion: Snoopy is not a dog | Snoopy is not a mammal. |
| Write the first four terms of an arithmetic sequence if a1=-2 and the common diffence is -4 | -2, -6, -10, -14 |
| Write the first four terms of an geometric sequence if a1=-2 and the common ratio is -4 | -2, 8, -32,128 |
| Find the common ratio in the following geometric sequence 1/2, 1/3, 2/9, 4/27 | 2/3 |
| Find the common difference in the following arithmetic sequence 10, 4, -2, -8 | -6 |
| Find the value of the 15th term of the arithmetic sequence whose beginning term and -5 and common difference -4. | -5+(14)*(-4) = -61 |
| Find the value of the 6th term of the geometric sequence whose beginning term and -3 and common ratio 2. | (-3)*(2)^5=-96 |
| The following sequence has a pattern, What is the next term in the sequence? 40, 10, 2, 1/3 | Multiply by 1/4,1/5,1/6, 1/7.....(1/3)*(1/7)=1/21 |
| Inductive or Deductive Reasoning? Everytime you throw a rock in the lake it sinks. You conjecture that "All rocks sink" | Inductive |
| Inductive or Deductive Reasoning? Complementary angles have a sum of 90 degrees. If one angle is 60 degrees you conclude its complementary angles measures 30 degrees. | Deductive |
| The following sequence has a pattern, What is the next term in the sequence? 2,4,12,48, | times 2, times 3, times 4....48 times 5 =240 |
| A conditional statement and its _______________are logically equivalent | Contrapositive |
| The converse of a statement an _____________of a statement are logically equivalent. | Inverse |
| Write a statement logically equivalent to the following. "If an object glitters, then the object is made of gold" | The contrapositive is logically equivalent. " If an object is not made of gold, then the object does not glitter. |
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