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(b) The following is a proposed proof of the given statement. 1. Suppose m is any even integer and n is any odd integer. 2. If m · n is even, then by definition of even there exists an integer r such that m n = 2r. 3. Also sincem is even, there exists an integer p such that m = 2p by definition of even. 4. And sincen is odd, there exists an integer q such that n = 2g + 1 by definition of odd. 5. Thus, by substitution, m n = (2p)(2q + 1) = 2r, where r is an integer. 6. Hence, by definition of even, then, m•n is even, as was to be shown. Reorder the sentences in the following scrambled list to explain the mistake in the proposed proof. Step 5 deduces a conclusion that would be true if S were known to be true. Hence, the proposed proof is circular; it assumes what is to be proved. Let S be the sentence, "There is an integer r such that m·n equals 2r." The truth of S is not known at the point where Step 5 occurs because the assumption that m n is even has not been proved. Since the truth of Step 6 depends on the truth of the conclusion in Step 5, Step 6 is not a valid deduction. Step 2 states that the truth of S would follow from the assumption that m n is even. Thus, the conclusion in Step 5 is not a valid deduction. Select appropriate sentences from the list and put them in the correct order to explain the mistake in the proposed proof. 1. Let S be the sentence, "There is an integer r such that m - n equals 2r." 2. Step 2 states that the truth of S would follow from the assumption that m n is even. 3. -Select--- 4. Select.. 5. Step 5 deduces a conclusion that would be true if S were known to be true. 6. Select-- 7. Hence, the proposed proof is circular; it assumes what is to be proved.

(b) The following is a proposed proof of the given statement. 1. Suppose m is any even integer and n is any odd integer. 2. If m · n is even, then by definition of even there exists an integer r such that m n = 2r. 3. Also sincem is even, there exists an integer p such that m = 2p by definition of even. 4. And sincen is odd, there exists an integer q such that n = 2g + 1 by definition of odd. 5. Thus, by substitution, m n = (2p)(2q + 1) = 2r, where r is an integer. 6. Hence, by definition of even, then, m•n is even, as was to be shown. Reorder the sentences in the following scrambled list to explain the mistake in the proposed proof. Step 5 deduces a conclusion that would be true if S were known to be true. Hence, the proposed proof is circular; it assumes what is to be proved. Let S be the sentence, "There is an integer r such that m·n equals 2r." The truth of S is not known at the point where Step 5 occurs because the assumption that m n is even has not been proved. Since the truth of Step 6 depends on the truth of the conclusion in Step 5, Step 6 is not a valid deduction. Step 2 states that the truth of S would follow from the assumption that m n is even. Thus, the conclusion in Step 5 is not a valid deduction. Select appropriate sentences from the list and put them in the correct order to explain the mistake in the proposed proof. 1. Let S be the sentence, "There is an integer r such that m - n equals 2r." 2. Step 2 states that the truth of S would follow from the assumption that m n is even. 3. -Select--- 4. Select.. 5. Step 5 deduces a conclusion that would be true if S were known to be true. 6. Select-- 7. Hence, the proposed proof is circular; it assumes what is to be proved.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with 3,4,5 and 6
(b) The following is a proposed proof of the given statement. 1. Suppose m is any even integer and n is any odd integer. 2. If m · n is even, then by definition of even there exists an integer r such that m·n = 2r. 3. Also sincem is even, there exists an integer p such that m = 2p by definition of even. 4. And sincen is odd, there exists an integer q such that n = 2g + 1 by definition of odd. 5. Thus, by substitution, m n = (2p)(2q + 1) = 2r, where r is an integer. 6. Hence, by definition of even, then, m•n is even, as was to be shown. Reorder the sentences in the following scrambled list to explain the mistake in the proposed proof. Step 5 deduces a conclusion that would be true if S were known to be true. Hence, the proposed proof is circular; it assumes what is to be proved. Let S be the sentence, "There is an integer r such that m·n equals 2r." The truth of S is not known at the point where Step 5 occurs because the assumption that m n is even has not been proved. Since the truth of Step 6 depends on the truth of the conclusion in Step 5, Step 6 is not a valid deduction. Step 2 states that the truth of S would follow from the assumption that m n is even. Thus, the conclusion in Step 5 is not a valid deduction. Select appropriate sentences from the list and put them in the correct order to explain the mistake in the proposed proof. 1. Let S be the sentence, "There is an integer r such that m - n equals 2r." 2. Step 2 states that the truth of S would follow from the assumption thatm n is even. 3. -Select--- 4. Select.. 5. Step 5 deduces a conclusion that would be true if S were known to be true. 6. Select-- 7. Hence, the proposed proof is circular; it assumes what is to be proved.
Transcribed Image Text:(b) The following is a proposed proof of the given statement. 1. Suppose m is any even integer and n is any odd integer. 2. If m · n is even, then by definition of even there exists an integer r such that m·n = 2r. 3. Also sincem is even, there exists an integer p such that m = 2p by definition of even. 4. And sincen is odd, there exists an integer q such that n = 2g + 1 by definition of odd. 5. Thus, by substitution, m n = (2p)(2q + 1) = 2r, where r is an integer. 6. Hence, by definition of even, then, m•n is even, as was to be shown. Reorder the sentences in the following scrambled list to explain the mistake in the proposed proof. Step 5 deduces a conclusion that would be true if S were known to be true. Hence, the proposed proof is circular; it assumes what is to be proved. Let S be the sentence, "There is an integer r such that m·n equals 2r." The truth of S is not known at the point where Step 5 occurs because the assumption that m n is even has not been proved. Since the truth of Step 6 depends on the truth of the conclusion in Step 5, Step 6 is not a valid deduction. Step 2 states that the truth of S would follow from the assumption that m n is even. Thus, the conclusion in Step 5 is not a valid deduction. Select appropriate sentences from the list and put them in the correct order to explain the mistake in the proposed proof. 1. Let S be the sentence, "There is an integer r such that m - n equals 2r." 2. Step 2 states that the truth of S would follow from the assumption thatm n is even. 3. -Select--- 4. Select.. 5. Step 5 deduces a conclusion that would be true if S were known to be true. 6. Select-- 7. Hence, the proposed proof is circular; it assumes what is to be proved.
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