2.1-2.4 Flashcards Preview

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Flashcards in 2.1-2.4 Deck (23):
1

Negation

Opposite of your original statement

2

When are your conditionals false

When you can provide a counter example

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Converse

When you exchange your hypothesis and conclusion
Ex if the car is red then it flys
If the car flys then it is red

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Inverse

Take the opposite of your original statement
Ex if the car is red then it flys
If the car is not red then it doesn't fly

5

Contrapositive

Write the converse and then take the opposite of that statement
Ex if the car is red then it flys
If the car doesn't fly then the car isn't red

6

Equivalent statements

When two statements are both true or both false they are called equivalent statements. Conditional and Contrapositive
Inverse and converse

7

Biconditional statements

If and only if

8

Inductive reasoning

A conjecture based on a pattern or observations, inferring

9

Deductive reasoning

Gives the facts, definitions, accepted properties, and laws of logic to form a logical conclusion

10

Law of detachment

If the hypothesis of a conditional statement is true then the conclusion is true
Ex if this wind keeps up then we will lose some trees. We lose some trees

Conclusion, the wind kept up

11

Law of syllogism

If the hypothesis is the same as the conclusion of another one.
Hypothesis P, conclusion Q,
Hypothesis Q, conclusion R
= hypothesis P conclusion R

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Conditional statement

An if then statement that has a hypothesis and conclusion

13

Postulate 5

Through any two points there exists exactly one line

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Postulate 6

A line contains at least two points

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Postulate 7

If two lines intersect then their intersection is exactly one point

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Postulate 8

Through any three noncollinear points there exists exactly one plane

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Postulate 9

A plane contains at least three noncollinear points

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Postulate 10

If two points lie in a plane then the line containing them lies in the plane

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Postulate 11

If two plane intersect then their intersection is a line

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Conjecture

A statement based on incomplete Info

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To make a conjecture true you must..

Show it is true for all cases

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To make a conjecture false you must...

Find one counter example

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A counter example is

A specific case for which the conjecture is false