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# DG Unit 2

### Vocab Chapter 2 Discoverying Geometry

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.
Created by: krolakd