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Title: Conditional%20Statements


1
Conditional Statements
  • Section 2-2

2
Objective
  • Students will be able to recognize conditional
    statements and their parts to write converses,
    inverses, and contrapositives of conditionals.

3
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)

4
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
6
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.

7
  • 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.

9
Using a Venn Diagram to illustrate a conditional
Illinois Residents
Chicago Residents
If you live in Chicago, then you live in Illinois.
10
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.

11
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! ?

12
The new stuff for today
  • negation the denial of a statement (the
    opposite)
  • Ex. An angle is obtuse.
  • Negation An angle is not obtuse.

13
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.

14
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.

15
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!
16
Assignment
  • P. 93 (15-45) xs of 3
  • Ask me about the OPTIONAL project!
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