Inductive Reasoning

Inductive Reasoning ,[object Object],[object Object],[object Object],[object Object]

Writing Conjectures ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Given:

[object Object],[object Object],[object Object],[object Object],Are the conjectures true? Find one counterexample

Are the conjectures true? ,[object Object],[object Object],[object Object],[object Object],Find one counterexample

[object Object],[object Object],[object Object],Are the conjectures true? Find one counterexample

Conjunctions and Disjunctions ,[object Object],p q ,[object Object],[object Object],p p q q Λ ν

Negations ,[object Object],p q ,[object Object],[object Object],p p q q Λ ν ~ ~

Paper 50 Cans 30 10 Communities that recycle VENN DIAGRAM

TRUTH TABLE ,[object Object],p q F F F F T F T F T F F T T T T T p ν q p Λ q q p

TRUTH TABLE ,[object Object],p q r F F F F F T F T F F F F F T F T F T T F F F F F T T F T F T T T F T T T T T T T ( p Λ q ) ν r p Λ q r q p

Conditionals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Hypothesis Conclusion IF THEN

Write Conditionals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Hypothesis Conclusion IF THEN

Conditional ,[object Object],[object Object],[object Object],[object Object],[object Object],Hypothesis Conclusion

Converse ,[object Object],[object Object],Conditional Converse

Inverse ,[object Object],[object Object],Conditional Inverse

Contrapositive ,[object Object],[object Object],Conditional Contrapositive

Converse ,[object Object],[object Object],Conditional Inverse

Write Conditionals ,[object Object],[object Object],[object Object],[object Object],[object Object]

Law of Detachment ,[object Object],[object Object],[object Object],Valid p q p q IF THEREFORE THEN

Law of Detachment ,[object Object],[object Object],[object Object],Invalid p q q p IF THEREFORE THEN

Law of Detachment ,[object Object],[object Object],[object Object],p q q p IF THEREFORE THEN It's a duck It flies It flies It's a duck

Law of Detachment ,[object Object],[object Object],[object Object],It's a bird It has wings It has wings It's a bird It's a bird It has wings

Law of Detachment ,[object Object],[object Object],[object Object],Invalid A B B A IF THEREFORE THEN

Law of Syllogism ,[object Object],[object Object],[object Object],[object Object],Valid p q p r IF THEREFORE THEN q r IF THEN

Law of Syllogism ,[object Object],[object Object],[object Object],[object Object],Invalid A B C B IF THEREFORE THEN B C IF THEN

Law of Syllogism ,[object Object],[object Object],[object Object],[object Object],Invalid p q r p IF THEREFORE THEN q r IF THEN

Law of Syllogism ,[object Object],[object Object],[object Object],[object Object],Valid A B A B IF THEREFORE THEN B C IF THEN

IF IF THEN THEN It's a bird It has wings It has wings It's a bird It's a bird It has wings It lays eggs It lays eggs It lays eggs THEREFORE

Deductive Reasoning ,[object Object],[object Object],[object Object]

Deductive Reasoning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Postulates ,[object Object],[object Object],[object Object],[object Object]

Postulates ,[object Object],[object Object],[object Object]

Properties of Equality ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Name the property ,[object Object],[object Object],[object Object],[object Object]

2 Column Proof Given: 3x + 5 2 Prove: x = 3 = 7 Statements Reasons

Properties of Segments ,[object Object],[object Object],[object Object]

Properties of Angles ,[object Object],[object Object],[object Object]

Segment Postulates ,[object Object],[object Object]

Properties of Segment Congruence ,[object Object],[object Object],[object Object]

Angle Postulates ,[object Object],[object Object]

Angle Theorems ,[object Object],[object Object],[object Object],[object Object],[object Object]

Name the property ,[object Object],[object Object],[object Object],[object Object],[object Object]

2 Column Proof Given: PR = QS Prove: PQ = RS Statements Reasons P Q R S

Inductive Reasoning

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Inductive Reasoning