Section 2.1 Notes

1. Section 2.1 Notes Conditional Statements

2. Conditional Statement • A type of logic statement that has two parts: a hypothesis and a conclusion • We will write the conditional statements in If-Then Form. When written in this form the ifpart is the _____________ and the then part is the ____________. hypothesis conclusion

3. Example 1: Write in If-Then form and state the hypothesis and conclusion • Two points are collinear if they lie on the same line. If-Then Form: Hypothesis:______________________ Conclusion:_________________ If two points lie on the same line, then they are collinear. Two points lie on the same line they are collinear

4. Example 2: Write in If-Then form and state the hypothesis and conclusion 2) All mammals breathe oxygen. If-Then Form: Hypothesis:_______________ Conclusion:_______________ If an animal is a mammal, then it breathes oxygen. an animal is a mammal it breathes oxygen

5. More Logic Definitions negation • The negative of a statement is the _________. Its symbol is the ~. (tilda) • ____________ is a statement formed by switching the hypothesis and the conclusion of a conditional statement. • ________ is a statement formed by negating the hypothesis and the conclusion of a conditional statement. • _____________ is a statement formed by negating the hypothesis and the conclusion of the converse of a conditional statement. Converse Inverse Contrapositive

6. Example 3: Write each statement and decide T or F 1) Conditional Statement: If m<A = 30°, the <A is acute. Converse: _____________________________ Inverse:_______________________________ Contrapositive:_________________________ If <A is acute, then the m<A = 30 º False, because an acute angle can be from 0 to 89.9 If m<A ≠ 30 º, then <A is not acute False, could be a 20o angle If <A is not acute, then m<A≠ 30 º True

7. Example 4: Write each statement and decide T or F 2) Conditional Statement: If an animal is a fish, then it can swim. Converse: _____________________________ Inverse:_______________________________ Contrapositive:_________________________ If an animal can swim, then it is a fish False; other animals can swim (turtle) If an animal is not a fish, then it can’t swim False; other animals can swim (turtle) If an animal can’t swim, then it is not a fish True

8. When two statements are both true or both false, they are called • In the ex 3 and 4, which statements are equivalent? equivalent statements Contrapositive and C.S. Converse and Inverse Example 1: This will always be the case Example 2: C.S. and Contrapositive Converse and Inverse

9. Point, Line, and Plane Postulates • Postulate 5: Through any two points there exists exactly _______________. • Postulate 6: A _______ contains at least two points. • Postulate 7: If two lines intersect, then their intersection is exactly ___________. • Postulate 8: Through any three noncollinear points there exists exactly ______________. one line line one point one plane

10. Postulates ctd. plane • Postulate 9: A _________ contain at least three noncollinear points. • Postulate 10: If two points lie in a plane, then the line containing them lies in the _________. • Postulate 11: If two planes intersect, then their intersection is a __________. plane a line