2.1-2.4 Flashcards
Negation
Opposite of your original statement
When are your conditionals false
When you can provide a counter example
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
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
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
Equivalent statements
When two statements are both true or both false they are called equivalent statements. Conditional and Contrapositive
Inverse and converse
Biconditional statements
If and only if
Inductive reasoning
A conjecture based on a pattern or observations, inferring
Deductive reasoning
Gives the facts, definitions, accepted properties, and laws of logic to form a logical conclusion
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
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
Conditional statement
An if then statement that has a hypothesis and conclusion
Postulate 5
Through any two points there exists exactly one line
Postulate 6
A line contains at least two points
Postulate 7
If two lines intersect then their intersection is exactly one point
