Fundamentals of Math - old

Fundamentals of Mathematics

8.2 Conditional Statements We just finished discussing in section 8.1 that a conditional statement is the joining of two sentences using the format If then . From this conditional statement ( → ), we can create three related statements: converse, inverse, or contrapositive.

• The converse of the conditional statement is, “If then .”

• The inverse of the conditional statement is, “If not then not .”

• The contrapositive of the conditional statement is, “If not then not .”

For example, assume the original conditional statement says, “If it snowed last night, then the sidewalk is frozen.” Therefore, is "it snowed last night," and is "the sidewalk is frozen. This means ... • The converse ( → ) is, “If the sidewalk is frozen, then it snowed last night.” • The inverse ( ~ → ~ ) is, “If it did not snow last night, then the sidewalk is not frozen.” • The contrapositive ( ~ → ~ ) is, “If the sidewalk is not frozen, then it did not snow last night.”

Example 8.2

Write the converse, the inverse, and the contrapositive of the conditional statement. Then tell whether each statement is true or false.

If the dog is a Saint Bernard, then it is large.

1. Converse: If the dog is large then it is a Saint Bernard. False – There are multiple large dog breeds besides Saint Bernard (i.e., Great Danes or Bernese Mountain dogs) 2. Inverse: If the dog is not a Saint Bernard, then it is not large. False - There are multiple large dog breeds besides Saint Bernard (i.e., Great Danes or Bernese Mountain dogs)

3. Contrapositive: If a dog is not large, then it is not a Saint Bernard. True – All Saint Bernards are classified as large dogs.

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