Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Appendix: Inductive and Deductive Reasoning - Appendix Exercises: 16

Answer

The conclusion follows the premises. Refer to the diagram below.
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Work Step by Step

The Euler's circles for the first statement involve the circle for Students being inside the circle for Hard Workers. All Business Majors are hard workers so the circle that represents Business Majors is inside the circle that represents the Students. Thus, the diagram will involve three circles: (1) The smallest circle, which is inside the circle that represents Students, represents the Business Majors. (2) The medium circle, which is inside the circle that represents Hard Workers, represents all Students. (3) The biggest circle, which contains both smaller circles, represents Hard Workers. (Refer to the diagram in the answer part above.) The diagram shows that all Business Majors are hard Workers. Thus, the conclusion follows the premises.
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