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Section 2.1 Conditional Statements

Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

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Page 1: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Section 2.1

Conditional Statements

Page 2: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Conditional Statement

A sentence in if-then form.

“If” part – hypothesis

“Then” part – conclusion

Page 3: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Example

If you are at school, then it is a weekday.

If P, then Q.

Page 4: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Example

Rewrite as a conditional.a. Two points are collinear if they lie of the same line.

b. All sharks have boneless skeletons.

c. A number divisible by 9 is also divisible by 3.a.If two points are collinear,

c.If a number is divisible by 9,

b.If it is a shark,

then they lie in the same line.

then it has a boneless skeleton.

then it is divisible by 3.

Page 5: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Counterexample

An example that shows a conditional statement is false.

Page 6: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Example

Find a counterexample.

If a number is odd, then it is divisible by 3.

5, 7, etc. are odd numbers, but not divisible by 3.

(Need only one)

Page 7: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Converse

Formed by switching the hypothesis and conclusion.

If Q, then P.

If it is raining, then it is cloudy.P Q

Conditional:

If it is cloudy, then it is raining.

Page 8: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Inverse

Formed by negating the hypothesis and conclusion.

If it is raining, then it is cloudy.P Q

Conditional:

If not P, then not Q.

If it is not raining, then it is not cloudy.

Page 9: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Contrapositive

Formed by switching and negating the hypothesis and conclusion.

If it is raining, then it is cloudy.P Q

Conditional:

If not Q, then not P.

If it is not cloudy, then it is not raining.

Page 10: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

Some Important Postulates

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

Postulate: Through any three non-collinear points there exists exactly one plane.

Page 11: Section 2.1 Conditional Statements. Conditional Statement A sentence in if-then form. “If” part – hypothesis “Then” part – conclusion

p. 75:

9-10, 14-17,

19, 22, 25-28

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