2'3 Conditional Statements 10509

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2.3 Conditional Statements 10/5/09

• Truth Values of Conditionals
• Determine the truth value of the following
  statement for each set of conditions.
• If you get 100 on your test, then your teacher
  will give you an A.
• a. You get 100 on your test your teacher gives
  you an A.
• The hypothesis is true because you received
  100 on your test. Your conclusion is
  true because the teacher gives you an A.
  Since what the teacher promised is true,
  the conditional statement is true.
• b. You get 100 on your test your teacher gives
  you a B.
• The hypothesis is true. The conclusion is
  false. Because the result is not what
  was promised, the conditional statement
  is false.

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• Determine the truth value of the following
  statement for each set of conditions.
• If you get 100 on your test, then your teacher
  will give you an A.
• c. You get 98 on your test your teacher gives
  you an A.
• The hypothesis is false, and the conclusion is
  true. The statement does not say what
  will happen if you do not have a 100 on
  the test. You could still get an A. It is
  also possible that you can get a B. In this
  case, we cannot say if the statement is
  false. So, the statement is true.
• d. You get 85 on your test your teacher gives
  you a B.
• As in part c, we cannot say that the statement
  is false. Therefore, the conditional
  statement is true.

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Related Conditionals

• Related conditionals are other statements based
  on a given conditional statement.

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Related Conditionals
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Related Conditionals

• Examples
• Conditional if two angles have the same
  measure, then they are congruent.
• Converse if two angles are congruent, then they
  have the same measure.
• Inverse if two angles do not have the same
  measure, then they are not congruent.
• If two angles are not congruent, then they do not
  have the same measure.
• Logically equivalent statements with the same
  truth values.

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Truth Tables
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Related Conditionals

• Write the converse, inverse, and contrapositive
  of the statement Linear pairs of angles are
  supplementary. Determine whether each statement
  is true or false. If the statement is false,
  give a counterexample.
• First, write the conditional in if then form.
• Conditional If two angles form a linear pair,
  then they are supplementary.
• The conditional statement is true.

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Related Conditionals

• Write the converse, inverse, and contrapositive
  of the statement Linear pairs of angles are
  supplementary. Determine whether each statement
  is true or false. If the statement is false,
  give a counterexample.
• Converse If two angles are supplementary, then
  they form a linear pair. Angles can add up to
  180, but do not have to be a linear pair.
• Inverse If two angles do not form a linear
  pair, then they are not supplementary. The
  inverse is false. Two angles can add to 180,
  but do not have to be a linear pair.
• Contrapositive If two angles are not
  supplementary, then they do not form a linear
  pair. The contrapositive is true.

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Homework!!!

• S.G. 2.1 and 2.3