2'1 Ifthen Statements, converses 6'2 Inverses and Contrapositives

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2.1 If-then Statements, converses6.2
Inverses and Contrapositives
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If-then statements are called conditionals

• If it rains after school, I will give you a ride
  home.
• If part is called the hypothesis p
• Then part is called the conclusion q
• Notation for a conditional p?q
• Read if p, then q

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Converse q?p

• The converse is formed by interchanging the
  hypothesis and the conclusion
• If it rains after school, I will give you a ride
  home.
• If I give you a ride home, then it rains after
  school

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• Identify the hypothesis and the conclusion. Give
  the converse.
• If an angle is 140, then it is obtuse.
• If you wear Nike shoes, youll run faster.
• When you wear Abercrombie clothes, you are be
  popular.
• Everyone will want to be your friend if you get
  an A in Geometry.

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Counterexamples

• A conditional or converse is false is an example
  can be found for which the hypothesis is true and
  the conclusion is false. This is a
  counterexample.
• If I live in Cary, I live in North Carolina.
• If x² 4, then x 2

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Biconditional

• A statement that contains the words if and only
  if
• The conditional and the converse are true
• All definitions are biconditionals
• Notation iff reads if and only if
• ?
• A right angle measures 90.
• Congruent segments are segments that have equal
  lengths

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Inverse p?q

• means not
• p ? q reads if not p, then not q
• The intersection of two planes is a line.

Contrapositive q ?p
Is the contrapositive the logical equivalent of
the conditional?
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If m?A 140, then it is obtuse.

• Conditional
• Converse
• Inverse
• Contrapositive

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Venn diagrams