Lesson 2.2 Analyze Conditional Statements

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Lesson 2.2 Analyze Conditional Statements

• Goal The learner will write definitions as
  conditional statements.

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Vocabulary

• Conditional Statement a logical statement that
  has a hypothesis and a conclusion.
• If-then form format for a conditional
  statement.
• Hypothesis the if part
• Conclusion the then part
• Hypothesis must always be true.

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Example

• If it is raining, then there are clouds in the
  sky.
• If the car is a Mustang, then it is a Ford.

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Writing Conditional Statements

• All birds have feathers.
• Two angles are supplementary if they are a linear
  pair.

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More Examples

• All 90 angles are right angles.
• When n 9, n² 81.
• Tourists at the Alamo are in Texas.

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Negation the opposite of the original statement.

• The ball is red.
• Negation
• The cat is not black.
• Negation

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Converse flip-flop the hypothesis and
conclusion.

• If it is raining, then I will carry an umbrella.
• Converse
• If I am in Roadtown, then Im in Tortola.
• Converse

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Inverse Negate both the hypothesis and
conclusion

• If it is a Corvette, then it is a Chevy.
• Inverse
• If you are a soccer player, then you are an
  athlete.
• Inverse

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Contrapositive negate and flip-flop the
hypothesis and conclusion.
Converse Inverse Contrapositive
Are these statements true?
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Verifying Statements

• You must show the conclusion is true every time
  the hypothesis is true.
• It only takes one counterexample to show its
  false.

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Use Guitar players are musicians. to write the
following.

• If-then
• Converse
• Inverse
• Contrapositive

Which statements are true? Give a counterexample
if it is false.
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• If a polygon is equilateral, then the polygon is
  regular.
• Converse
• Inverse
• Contrapositive

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Equivalent Statements when two statements are
both true or false.

• Conditional Statement and its contrapositive are
  either both true or false.
• Converse and inverse are either both true or
  false.

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Definitions as Conditional Statments

• Any definition can be written as if-then or as
  its converse.
• Example
• Right Angles If the angle measure is 90?, then
  it is a right angle.

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Biconditional Statement When a If-Then and its
converse are true you can write them as a single
statement.

• All definitions are biconditional.
• Example
• Perpendicular lines If the angle measure is
  90?, then then it is a right angle.
• Converse If the angle is a right angle, then the
  its measure is 90?.
• Biconditional An angle is a right angle if and
  only if the its measure is 90?

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Example

• Write the definition of straight angle as a
  biconditional statement.

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Another Example

• If Mary is in theater class, she will be in the
  fall play. If Mary is in the fall play, she must
  be taking theater class.