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Chapter 2. Section 2.1 Conditional Statements. Conditional Statement. Type of logical statement 2 parts Hypothesis/Conclusion Usually written in “if-then” form If George goes to the market , then he will buy milk. Hypothesis. Conclusion.

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chapter 2

Chapter 2

Section 2.1

Conditional Statements

conditional statement
Conditional Statement
  • Type of logical statement
  • 2 parts
    • Hypothesis/Conclusion
  • Usually written in “if-then” form
    • If George goes to the market, then he will buy milk.

Hypothesis

Conclusion

If the hypothesis is true then the conclusion must be true

rewrite each conditional statement in if then form
Rewrite each conditional statement in if-then form
  • It is time for dinner if it is 6 pm.
    • If it is 6 pm, then it is time for dinner
  • There are 12 eggs if the carton is full
    • If the egg carton is full, then there are 12 eggs.
  • A number is divisible by 6 if it is divisible by 2 and 3.
    • If a number is divisible by 2 and 3, then it is divisible by 6
  • An obtuse angle is an agle that measures more than 90 and less than 180.
    • If an angle is obtuse then it measures more than 90 and less than 180.
  • All students taking geometry have math during an even numbered block
    • If you are taking geometry, then you have math during an even numbered block.
counter example
Counter Example
  • Used to prove a conditional statement is false
  • Must show an instance where the hypothesis is true and the conclusion is false.
    • Ex. If x2 = 9 then x = 3
    • Counter Ex. (-3)2 = 9, but –3,  3
  • Only need one counter example to prove something is not always true.
decide whether the statement is true or false if it is false give a counter example
Decide whether the statement is true or false. If it is false, give a counter example
  • The equation 4x – 3 = 12 + 2x has exactly one solution
    • True
  • If x2 = 36 then x = 18 or x = -18
    • False: (6)2 = 36 and 6  18 or 6  -18
  • Thanksgiving is celebrated on a Thursday
    • True
  • If you’ve visited Springfield, then you’ve been to Illinois.
    • False: If you’ve visited Springfield, then you’ve been to Massachusetts (Springfield MA.)
  • Two lines intersect in at most one point.
    • True
new statements formed from a conditional
New statements formed from a conditional
  • Converse: Switch the hypothesis and conclusion
    • Conditional: If you see lightning, then you hear thunder
    • Converse: If you hear thunder, then you see lightning
  • If you like hockey, then you go to the hockey game
    • If you go to the hockey game, then you like hockey
  • If x is odd, then 3x is odd
    • If 3x is odd, then x is odd
  • If mP = 90, then P is a right angle
    • If P is a right angle, then mP = 90
new statements formed from a conditional7
New statements formed from a conditional
  • Inverse: When you negate the hypothesis and conclusion of a conditional
  • Negate: To write the negative of a statement
    • Conditional: If you see lightning, then you hear thunder
    • Inverse: If you do not see lightning, then you do not hear thunder
  • If you like hockey, then you go to the hockey game
    • If you don’t like hockey, then you don’t go to the hockey game
  • If x is odd, then 3x is odd
    • If x is not odd, then 3x is not odd
  • If mP = 90, then P is a right angle
    • If mP  90, then P is not a right angle
new statements formed from a conditional8
New statements formed from a conditional
  • Contrapositive: When you switch and negate the hypothesis and conclusion of a conditional
    • Conditional: If you see lightning, then you hear thunder
    • Contrapositive: If you do not hear thunder, then you do not see lightning
  • If you like hockey, then you go to the hockey game
    • If you don’t go to the hockey game, then you don’t like hockey
  • If x is odd, then 3x is odd
    • If 3x is not odd, then x is not odd
  • If mP = 90, then P is a right angle
    • If P is not a right angle, then mP  90
equivalent statements
Equivalent Statements
  • When two statements are both true, they are called equivalent statements
point line and plane postulates
Point, Line, and Plane Postulates
  • Through any two points there exists exactly one line
  • A line contains at least two points
  • If two lines intersect, then their intersection is exactly one point (14)
  • Through any three noncollinear points there exists exactly one one plane
point line and plane postulates11
Point, Line, and Plane Postulates
  • A plane contains at least three noncollinear points
  • If two points lie in a plane, then the line containing them lies in the same plane (15)
  • If two planes intersect the, then their intersection is a line. (16)
use the diagram to state the postulate that verifies the statement
Use the diagram to state the postulate that verifies the statement
  • The points E, F, and H lie in a plane
    • Postulate #8: Through any three noncollinear points there exists one plane.
  • The points E and F lie on a line
    • Postulate #5: Through any two points there exists exactly one line
use the diagram to state the postulate that verifies the statement13
Use the diagram to state the postulate that verifies the statement
  • The planes Q and R intersect in a line
    • Postulate #11 If two planes intersect the, then their intersection is a line.
  • The points E and F lie in plane R. Therefore, line m lies in plane R
    • Postulate #10: If two points lie in a plane, then the line containing them lies in the same plane