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: 17

Answer

The conclusion does not follow the premises.
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Work Step by Step

The Euler's circles for the first statement involve the circle for Teachers being inside the circle for Serious. The Euler's circles for the second statement involve the circle for Mathematicians being inside the circle for Serious. Note, however, for mathematicians and teachers, there are two possible cases: (a) Some mathematicians are also teachers (and vice versa). (b) No mathematician is a teacher. The diagram will involve three circles: (1) One circle, which is inside the circle that represents Serious, represents the Teachers. (2) One circle, which is inside the circle that represents Serious, represents all Mathematicians. (3) The biggest circle, which contains both circles in (1) and (2) above, represents Serious. (Refer to the diagram in the answer part above.) The diagram shows that NOT all Mathematicians are Teachers. Thus, the conclusion does not follow the premises.
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