Select the mistake that is made in the proof given below. Theorem. The sum of two...
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Select the mistake that is made in the proof given below. Theorem. The sum of two odd integers is even. Proof. Since x is odd, x = 2k + 1 for some integer k. Since y is odd, y = 2j + 1, for some integer j. Plugging in the expression 2k + 1 for x and 2j + 1 for y into x + y gives x + y = (2k + 1) + (2j + 1) = 2k +2k + 2 = 2(k+j+1) Since k and j are integers, k+j+1 is also an integer. Therefore, since x + y is equal to 2m, where m=k+j+1 is an integer, x + y is even. ■ a. Generalizing from examples. b. Misuse of existential instantiation. c. Failure to properly introduce a variable. d. Assuming facts that have not yet been proven. Select the mistake that is made in the proof given below. Theorem. The sum of two odd integers is even. Proof. Since x is odd, x = 2k + 1 for some integer k. Since y is odd, y = 2j + 1, for some integer j. Plugging in the expression 2k + 1 for x and 2j + 1 for y into x + y gives x + y = (2k + 1) + (2j + 1) = 2k +2k + 2 = 2(k+j+1) Since k and j are integers, k+j+1 is also an integer. Therefore, since x + y is equal to 2m, where m=k+j+1 is an integer, x + y is even. ■ a. Generalizing from examples. b. Misuse of existential instantiation. c. Failure to properly introduce a variable. d. Assuming facts that have not yet been proven.
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Related Book For
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
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