Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-2 Conditional Statements - Got It?: 4

Answer

conditional - true converse - false inverse - false contrapositive - true

Work Step by Step

The hypothesis is, "A vegetable is a carrot." The conclusion is, "The vegetable contains beta carotene." The converse swaps the hypothesis and conclusion If a vegetable contains beta carotene then the vegetable is a carrot. The statement is false because sweet potatoes also contain beta carotene. The inverse negates the hypothesis and the conclusion. If a vegetable is not a carrot then the vegetable does not contain beta carotene. Again the statement is false because sweet potatoes also contain beta carotene. The contrapositive swaps the hypothesis and conclusion and negates both. If a vegetable does not contain beta carotene then the vegetable is not a carrot. Since all carrots contain beta carotene, this is a true statement.
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