Conditional Statements

1
Conditional Statements

• Conditional Statement If, then format.
• Converse Flipping the Logic
• Still if, then format, but we switch the
  hypothesis and conclusion
• Negation We can alter a statement by converting
  it to its negative form.
• Inverse Negating the hypothesis and conclusion
  of the original conditional statement
• Contra-positive Negating the hypothesis and
  conclusion of the of the Converse
• Equivalent Statements When two statements are
  both true or both false.
• A Conditional statement is equivalent to its
  contra-positive
• Similarly, an inverse and converse of any
  conditional statement will be equivalent.

2
Equivalent Statements

• Equivalent Statements When two statements are
  both true or both false.
• A Conditional statement is equivalent to its
  contra-positive
• Similarly, an inverse and converse of any
  conditional statement will be equivalent.
• Examples
• Conditional If an angle measures 30, then it is
  an acute angle. (True)
• Converse If an angle is an acute angle, then it
  measures 30. (False)
• Inverse If an angle does not measure 30, then it
  is not acute. (False)
• Contra-Positive If an angle is not an acute
  angle, then it does not measure 30. (True)

3
Point, Line, and Plane Postulates

• Postulate 5 Through any 2 points there exists
  exactly one line.
• Postulate 6 A line contains at least 2 points.
• Postulate 7 If 2 lines intersect, then their
  intersection is exactly one point.
• Postulate 8 Through any 3 non-collinear points
  there exists exactly one plane.
• Postulate 9 A plane contains at least 3
  non-collinear points.
• Postulate 10 If 2 points lie in a plane, then
  the line containing them lies in the plane.
• Postulate 11 If 2 planes intersect, then their
  intersection is a line.

4
Bi-conditional Statements

• Statements using the if and only if logic
  construct
• In other words, the conclusion can only be true ,
  if and only if the hypothesis holds.
• Again simply because the logic holds, does not
  make the bi-conditional stmt true
• Testing the logic
• Re-write the bi-conditional as
• A conditional statement,
• And its converse
• If BOTH are true, the bi-conditional is true.