Conditional%20Statements

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Conditional Statements

• Section 2-2

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Objective

• Students will be able to recognize conditional
  statements and their parts to write converses,
  inverses, and contrapositives of conditionals.

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Conditional Statements

• If-then statements are called conditional
  statements.
• The portion of the sentence following if is
  called the hypothesis. The part following then
  is called the conclusion.
• p q (If p, then q)

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p
q

• If it is an apple, then it is a fruit.
• Hypothesis It is an apple.
• Conclusion It is a fruit.
• A conditional can have a truth value of true or
  false.

5
Using a Venn Diagram to illustrate a conditional
q
p
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Converse q p

• The converse statement is formed by switching the
  hypothesis and conclusion.
• If it is an apple, then it is a fruit.
• Converse If it is a fruit, then it is an apple.
• The converse may be true or false.

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• Underline the hypothesis and circle the
  conclusion for each conditional statement, then
  write the converse.
• If you are an American citizen, then you have the
  right to vote.
• If a figure is a rectangle, then it has four
  sides.

8

• Write each sentence as a conditional statement.
• A point in the first quadrant has two positive
  coordinates.
• If a point is in the first quadrant, then it has
  two positive coordinates.
• Thanksgiving in the U.S. falls on the fourth
  Thursday of November.
• If it is Thanksgiving in the U.S., then it is the
  fourth Thursday of November.

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Using a Venn Diagram to illustrate a conditional
Illinois Residents
Chicago Residents
If you live in Chicago, then you live in Illinois.
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Get a Partner!

1. Each of you need to write 5 conditional
   statements and draw 5 venn diagrams
2. Trade papers
3. Write the converse of each conditional statement
   your partner wrote.

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Biconditionals

• Remember If your original conditional statement
  is true and your converse is true, then you can
  write a biconditional. p?q read as p if and
  only if q we can shorten it to p iff q.
• When either or both of your condition and the
  converse is false, then you must write a counter
  example. Why is it false?
• See page 78 for sample problems! ?

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The new stuff for today

• negation the denial of a statement (the
  opposite)
• Ex. An angle is obtuse.
• Negation An angle is not obtuse.

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Inverse p q

• An inverse statement can be formed by negating
  both the hypothesis and conclusion.
• If it is an apple, then it is a fruit.
• Inverse If it is not an apple, then it is not a
  fruit.
• The inverse may be true or false.

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Contrapositive q p

• A contrapositive is formed by negating the
  hypothesis and conclusion of the converse.
• If it is an apple, then it is a fruit.
• Contrapositive If it is not a fruit, then it is
  not an apple.
• The contrapositive of a true conditional is true
  and of a false conditional is false.

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Truth Table
Conditional Converse Inverse Contrapositive And or
p q p?q q ? p p ? q q ? p pnq pUq




T F T T
T F T T
T T F T
T T F T
T F F F
T T T F
T T T F F T F F
Which columns are congruent? These are called
equivalent statements, because they have the same
truth values!
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Assignment

• P. 93 (15-45) xs of 3
• Ask me about the OPTIONAL project!