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1. Create a flow proof of the following result: For every real number x, if (x − 3)² ≤ 0, then 10- x² > 0. - 2. For each of the following parts, consider the result: For every integer n, n is even if and only if 3n - 11 is odd. (a) Notice the result is a biconditional statement. Write out the two implications you need to show in order to prove the result. (b) Create two separate flow proofs, one for each of the implications you listed in part (a). (Hint: Use the technique proof of contrapositive for one of the implications.)

1. Create a flow proof of the following result: For every real number x, if (x − 3)² ≤ 0, then 10- x² > 0. - 2. For each of the following parts, consider the result: For every integer n, n is even if and only if 3n - 11 is odd. (a) Notice the result is a biconditional statement. Write out the two implications you need to show in order to prove the result. (b) Create two separate flow proofs, one for each of the implications you listed in part (a). (Hint: Use the technique proof of contrapositive for one of the implications.)

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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Recall in a flow proof, each step should be a single statement (in a box or on a line), and each arrow should be labeled with the appropriate justification (definition or property). 1. Create a flow proof of the following result: For every real number x, if (x - 3)² ≤ 0, then 10 - x² > 0. 2. For each of the following parts, consider the result: For every integer n, n is even if and only if 3n - 11 is odd. (a) Notice the result is a biconditional statement. Write out the two implications you need to show in order to prove the result. (b) Create two separate flow proofs, one for each of the implications you listed in part (a). (Hint: Use the technique proof of contrapositive for one of the implications.)
Transcribed Image Text:Recall in a flow proof, each step should be a single statement (in a box or on a line), and each arrow should be labeled with the appropriate justification (definition or property). 1. Create a flow proof of the following result: For every real number x, if (x - 3)² ≤ 0, then 10 - x² > 0. 2. For each of the following parts, consider the result: For every integer n, n is even if and only if 3n - 11 is odd. (a) Notice the result is a biconditional statement. Write out the two implications you need to show in order to prove the result. (b) Create two separate flow proofs, one for each of the implications you listed in part (a). (Hint: Use the technique proof of contrapositive for one of the implications.)
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