Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.

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Presentation transcript:

Inductive Reasoning Notes 2.1 through 2.4

Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is always larger than each of the 2 numbers. Counterexample – A specific case that makes the conjecture false EXAMPLE: (– 3) + (– 4) = – 7

Conditional Statements Conditional Statements – A logical statement that has 2 parts. Can be written in If, Then Form. Hypothesis – the “if” part Conclusion – the “then” part Example: If you have Ms. Brown is a teacher, you are in Geometry PAP.

Rewriting Conditional Statements All birds have feathers 2 angles are supplementary if they are a linear pair When n = 9, n 2 = 81

Changes to Conditional Statements Negation – the opposite of the original statement EX: You are a freshman => You are NOT a freshman Converse – Switches the order of the hypothesis and conclusion EX: If you are are 14, then you are a freshman If you are a freshman, then you are 14 Inverse – Negation of BOTH the hypothesis and conclusion EX: If you are 14, then you are a freshman If you are NOT 14, then you are NOT a freshman Contrapositive – Inverse of the Converse EX: If you are are 14, then you are a freshman If you are NOT a freshman, then you are NOT 14

Biconditional Statements Perpendicular Lines – If 2 lines intersect to form a right angles, then they are perpendicular lines. Can write using upside down T Biconditional Statements – when a conditional statement and it’s converse are both true, you can rewrite the statement to say “if and only if”

Deductive Reasoning Deductive Reasoning – uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

Quiz 1

Postulate5: Through any two points there exists exactly one line.

Postulate6: A line contains at least two points.

Postulate7: If two lines intersect, then their intersection is exactly one point.

Postulate8: Through any three noncollinear points there exists exactly one plane.

Postulate8: A plane contains at least three noncollinear points.

Postulate9: If two points lie in a plane, then the line containing them lies in the plane.

Postulate10: If two planes intersect, then their intersection is a line.