Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

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Reasoning and Proof DAY 3: 2.3 Biconditional Statements

description

bi- conditional iff ↔

Transcript of Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

Page 1: Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

Reasoning and ProofDAY 3: 2.3 Biconditional Statements

Page 2: Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

qp

~p~q

~q~p

If an animal has 4 legs, then it is a dog.

If an animal does not have 4 legs, then it is not a dog.

If an animal is not a dog, then it does not have 4 legs.

F

F

T

Page 3: Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

bi- conditional

iff↔

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If three points are collinear, then they lie on the same line.Three points lie on the same line iff they are collinear.

If I am skiing, then I am downhill skiing.Counterexample: waterskiing

Page 5: Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

reversiblecounterexample

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If two lines are perpendicular, then they intersect to form right angles.If two lines intersect to form right angles, then they are perpendicular.Two lines intersect are

perpendicular iff they intersect to form right angles.

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Good definitions: conditional and converse are true.

TrueFalse. Whale.

False. Rectangle.

False. Straight Angle.

True

True

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2.3 PRACTICEHomework:


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2.3 deductive reasoning

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Logical Reasoning zDeductive reasoning zInductive reasoning.

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2.3 Deductive Reasoning p. 87 Reminders Statement Conditional statement Converse Inverse Contrapositive Biconditional Symbols p → q q → p ~p → ~q ~q.

2.3 Deductive Reasoning p. 87 Reminders Statement Conditional statement Converse Inverse Contrapositive Biconditional Symbols p → q q → p ~p → ~q ~q.