Section 2.1 Notes

Conditional Statements

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 if part is the _____________ and the then part is the ____________.conclusion

hypothesis

Example 1: Write in If-Then form and state the hypothesis and conclusion

1) 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

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

More Logic Definitions 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.

negation

Converse

Inverse

Contrapositive

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

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)

False; other animals can swim (turtle)

True

If an animal is not a fish, then it can’t swim

If an animal can’t swim, then it is not a fish

Example 4: Write each statement and decide T or F

When two statements are both true or both false, they are called

In the ex 3 and 4, which statements are equivalent?

equivalent statements

Example 1:

Example 2:

Contrapositive and C.S.Converse and Inverse

C.S. and ContrapositiveConverse and Inverse

This will always be the case

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

Postulates ctd.

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

plane

a line