Answered: 1: Let p: “Chad is a good teacher.”, q:…

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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Question

1: Let p: “Chad is a good teacher.”, q: “Karen is a good teacher.”, r: “Chad's students hate math.”, and s: “Karen'students love math.” Express the following statements in words: 1. p∧∼r 6. ∼p∼q 2. p∨r∧∼q 7. r∨∼p∧q 3. q∨∼q 8. ∼p∼s∨q 4. r∧∼r 9. ∼s∼r 5. ∼q∨s 10. p∧r Activity No. 2: Construct the truth table for each of the following statements: 1. ~q⋀~p~r⋀r 2. (p⋀r⋁q⋀r)→r 3. ~~p→p⋀q 4. (q⋀~p→q)→p 5. ~r⋁q→~p⋀r Activity No. 3: For each of the following statements, construct a truth table and determine whether the following statement is a tautology, contradiction or contingency. 1.p→q⋁q→p 2.p⋁∼p⋀q⋁(~q) 3.p⋁~p 4.p⋁∼p⋀q⋁(~q) 5.~p⋀~q↔q Activity No. 4: For each of the following, construct a truth table to show the following pairs of statements are logically equivalent, contradictory, or unrelated statements: 1.~p→q and p⋀~q 2.q↔~p and p↔~q 3.p and p→q⋀~p 4.p⋀q→r and r→q⋁p 5.p⋁~q→~p⋀q and ~~p⋀q

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