2.1 Conditional Statements 2010
September 10, 2010
2­1 Conditional Statements
Objective
Write conditional statements and their converses.
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2.1 Conditional Statements 2010
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Check Skills You'll Need
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2.1 Conditional Statements 2010
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An If­Then statement is called a CONDITIONAL.
If you are not satisfied, then your money will be refunded.
Hypothesis
Conclusion
Identify the hypothesis and conclusion in the following conditional:
If today is the first day of fall, then the month is September.
Hypothesis: Today is the first day of fall
Conclusion: The month is September
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2.1 Conditional Statements 2010
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Write the following statements as conditionals:
A rectangle has four right angles.
If , then
A tiger is an animal.
An integer that ends in 0 is divisible by 5.
A square has four congruent sides.
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2.1 Conditional Statements 2010
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TRUTH VALUE
A conditional can have a truth value of true or false.
To show that a conditional is true, show that every time the hypothesis is true, the conclusion is also true.
TRUE
BUT, to show that a conditional is false, you need to find ONLY ONE counterexample for which the hypothesis is true and the FALSE
conclusion is false.
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Finding a Counterexample
Show that this conditional is false by finding a counterexample:
If it is February, then there are only 28 days in the month.
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CONVERSE
The CONVERSE of a conditional switches the hypothesis and the conclusion.
Conditional:
If two lines intersect to form right angles, then they are perpendicular.
Converse:
If two lines are perpendicular, then they intersect to form right angles.
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Write the converse of this conditional:
If two lines are not parallel and do not intersect, then they are skew.
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Finding the TRUTH VALUE of a CONVERSE
Which conditional statement has a false converse?
If two planes are parallel, then they have no points in common.
If a figure is a square, then it has four sides.
If a point has x-coordinate 0, then it lies on the y-axis.
If two angles are congruent, then they have the same measure.
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Conditional Statements and Converses
Statement
Example
Symbolic Form
You Read It
Conditional
If an angle is a straight angle,
then its measure is 180o.
p q
If p, then q.
Converse
If the measure of an angle is 180o, q p
then it is a straight angle.
If q, then p.
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Venn Diagrams
The set of things that satisfy the hypothesis lies inside the set of things that satisfy the conclusion.
Draw a Venn diagram to illustrate the conditional:
If you live in Chicago, then you live in Illinois
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HOMEWORK
p. 83 # 23 ­ 26, 27 ­ 35 odd
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