TABLE 1.6 Statement Correct Negation Incorrect Negation It will rain tomorrow. It is false that it will rain tomorrow. It will not rain tomorrow. It is false that Peter is tall Peter is short and fat. and thin. Peter is not tall or he is not thin. Peter is short or fat. Peter is tall and thin. Too strong a statement. Peter fails to have both properties (tallness and thinness) but may still have one property. The river is not shallow or not polluted. It is false that the river is shallow or polluted. The river is shallow or polluted. The river is neither shallow Too weak a statement. nor polluted. The river is deep and unpolluted. The river fails to have either property, not just fails to have one property.

TABLE 1.6 Statement Correct Negation Incorrect Negation It will rain tomorrow. It is false that it will rain tomorrow. It will not rain tomorrow. It is false that Peter is tall Peter is short and fat. and thin. Peter is not tall or he is not thin. Peter is short or fat. Peter is tall and thin. Too strong a statement. Peter fails to have both properties (tallness and thinness) but may still have one property. The river is not shallow or not polluted. It is false that the river is shallow or polluted. The river is shallow or polluted. The river is neither shallow Too weak a statement. nor polluted. The river is deep and unpolluted. The river fails to have either property, not just fails to have one property.

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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