2.1 – Conditional Statements Conditional Statement If-Then Form Hypothesis Conclusion Converse Negation Inverse Contrapositive Equivalent Statements

Conditional Statement A type of logical statement that has two

parts - a hypothesis and a conclusion

The if-then form of a conditional statement uses the words “if” and “then”. The “if” part contains the hypothesis and the “then” part contains the conclusion.

Hypothesis

The “if” part of a conditional statement

If Bill mows the lawn, then he will earn 20 dollars

Conclusion

The “then” part of a conditional statement

If Bill mows the lawn, then he will earn 20 dollars.

Converse The statement formed by

switching the hypothesis and the conclusion of a conditional statement

If you do your homework, then you will do well on the test.

If you do well on the test, then you did your homework.

• If you are in Massachusetts, then you are in New England.

• If you are in New England, then you are in Massachusetts.

• If you are in Hartford, then you are in Connecticut.

• If you are in Connecticut, then you are in Hartford.

Negation

The statement formed by writing the negative of the statement

The apple is red.

The apple is not red.

Inverse The statement formed when you negate the hypothesis and conclusion of a conditional statement

If Bill mows the lawn, then he will earn 20 dollars.If Bill does not mow the lawn, then he will not earn 20 dollars.

ContrapositiveThe statement formed when you negate the hypothesis and conclusion of the converse of a conditional statement

If Bill earned 20 dollars, then he mowed the lawn. If Bill did not earn 20 dollars, then he did not mow the lawn.

If we win the game, then we will be undefeatedConverse:If we are undefeated, then we won the

game.

Inverse: If we don’t win the game, then we will not

be undefeated.

Contrapositive:If we are not undefeated, then we did not

win the game.

Equivalent Statements When two statements are both true or both

false, they are called equivalent statements

Conditional statement: If an angle is 30 degrees, then it is acute.

Inverse: If an angle is not 30 degrees, then it is not acute.

Converse: If an angle is acute, then it is 30 degrees.

Contrapositive: If an angle is not acute, then it is not 30 degrees.

Point, Line, and Plan Postulates

Postulate 5 Through any two points there exists exactly one line.

Postulate 6 A line contains a least two points.

Postulate 7 If two lines intersect, then their intersection is exactly one point.

Postulate 8 Through any three noncollinear points there exists exactly one plane.

Point, Line, and Plan Postulates

Postulate 9 A plane contains at least three noncollinear points.

Postulate 10 If two points lie in a plane, then the line containing them lies in the plane.Postulate 11 If two planes intersect, then their

intersection is a line.