Prove the following statements with contrapositive proof. (In each case, think about how a direct proof would work. In most cases contrapositive is easier.) 1. Suppose n e Z. If n² is even, then n is even. 2. Suppose ne Z. If n2 is odd, then n is odd. 3. Suppose a, b e Z. If a²(b²-26) is odd, then a and b are odd. 4. Suppose a,b,c e Z. If a does not divide bc, then a does not divide b. 5. Suppose x E R. If x² +5x<0 then x < 0. 6. Suppose x E R. If x³ - 7. Suppose a, b e Z. If both ab and a +b are even, then both a and b are even. 8. Suppose x E R. If x5 - 4x4 +3x³ -x² + 3x-4≥0, then x ≥ 0. -x>0 then x>-1.

Prove the following statements with contrapositive proof. (In each case, think about how a direct proof would work. In most cases contrapositive is easier.) 1. Suppose n e Z. If n² is even, then n is even. 2. Suppose ne Z. If n2 is odd, then n is odd. 3. Suppose a, b e Z. If a²(b²-26) is odd, then a and b are odd. 4. Suppose a,b,c e Z. If a does not divide bc, then a does not divide b. 5. Suppose x E R. If x² +5x<0 then x < 0. 6. Suppose x E R. If x³ - 7. Suppose a, b e Z. If both ab and a +b are even, then both a and b are even. 8. Suppose x E R. If x5 - 4x4 +3x³ -x² + 3x-4≥0, then x ≥ 0. -x>0 then x>-1.

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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