Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

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Presentation transcript:

Reasoning and Proof DAY 3: 2.3 Biconditional Statements

qpqp ~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

biconditional iff ↔

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

reversible counterexample

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.

Good definitions: conditional and converse are true. True False. Whale. False. Rectangle. False. Straight Angle. True

2.3 PRACTICE Homework: