Chapter 2

							    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



If the hypothesis is true then the conclusion must be true
       Rewrite each conditional statement in if-then form

1. It is time for dinner if it is 6 pm.
   •     If it is 6 pm, then it is time for dinner
2. There are 12 eggs if the carton is full
   •     If the egg carton is full, then there are 12 eggs.
3. 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
4. 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.
5. 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
• 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
6. The equation 4x – 3 = 12 + 2x has exactly one
   solution
   •   True
7. If x2 = 36 then x = 18 or x = -18
   •   False: (6)2 = 36 and 6  18 or 6  -18
8. Thanksgiving is celebrated on a Thursday
   •   True
9. 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.)
10. Two lines intersect in at most one point.
   •   True
         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


11. If you like hockey, then you go to the hockey game
    •     If you go to the hockey game, then you like hockey
12. If x is odd, then 3x is odd
    •     If 3x is odd, then x is odd
13. 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
                   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
11. 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
12. If x is odd, then 3x is odd
    •     If x is not odd, then 3x is not odd
13. 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
                   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
11. 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
12. If x is odd, then 3x is odd
    •     If 3x is not odd, then x is not odd
13. If mP = 90, then P is a right angle
    •     If P is not a right angle, then mP  90
           Equivalent Statements
   • When two statements are both true, they are
     called equivalent statements

Original       If mA = 30, then A is acute
Inverse        If mA  30, then A is not acute
Converse       If A is acute, then mA = 30
Contrapositive If A is not acute, then mA  30
Point, Line, and Plane Postulates
5. Through any two points there exists
   exactly one line
6. A line contains at least two points
7. If two lines intersect, then their
   intersection is exactly one point (14)
8. Through any three noncollinear points
   there exists exactly one one plane
Point, Line, and Plane Postulates
9. A plane contains at least three noncollinear
    points
10. If two points lie in a plane, then the line
    containing them lies in the same plane (15)
11. If two planes intersect the, then their
    intersection is a line. (16)
       Use the diagram to state the postulate that verifies
                            the statement
17. The points E, F, and H lie in a
    plane
   •     Postulate #8: Through any three
         noncollinear points there exists one
         plane.
18. 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 statement
19. The planes Q and R intersect in
    a line
   •     Postulate #11 If two planes
         intersect the, then their intersection
         is a line.
20. 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
           HW #15
Pg 75-78 10-50 Even, 51, 55, 56