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old." The 20. Write negations for each of the following statements. (Assume that all variables represent fixed quantities or enti- ties, as appropriate.) ote" to be true. a. If P is a square, then P is a rectangle. b. If today is New Year's Eve, then tomorrow is January. c. If the decimal expansion of r is terminating, then r is How rational.

old." The 20. Write negations for each of the following statements. (Assume that all variables represent fixed quantities or enti- ties, as appropriate.) ote" to be true. a. If P is a square, then P is a rectangle. b. If today is New Year's Eve, then tomorrow is January. c. If the decimal expansion of r is terminating, then r is How rational.

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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How do you do number 20. Questions a,b, c, d and those statements contrapositives?
ot contain → 9 2.2.3, llow- real uiv- your ally to JS. u s no12 If it walks like a duck and it talks like a duck, then it is a duck. Either it does not walk like a duck or it does not talk like a duck, or it is a duck. If it does not walk like a duck and it does not talk like a duck, then it is not a duck. 19. True or false? The negation of "If Sue is Luiz's mother, then Ali is his cousin" is "If Sue is Luiz's mother, then Ali is not his cousin." years old. 20. Write negations for each of the following statements. (Assume that all variables represent fixed quantities or enti- ties, as appropriate.) a. If P is a square, then P is a rectangle. b. If today is New Year's Eve, then tomorrow is January. c. If the decimal expansion of r is terminating, then r is rational. d. If n is prime, then n is odd or n is 2. e. If x is nonnegative, then x is positive or x is 0. f. If Tom is Ann's father, then Jim is her uncle and Sue is her aunt. g. If n is divisible by 6, then n is divisible by 2 and n is divisible by 3. 21. Suppose that p and q are statements so that p →q is false. Find the truth values of each of the following: a.~p q b. pvq c. q→ P H 22. Write contrapositives for the statements of exercise 20. H 23. Write the converse and inverse for each statement of exercise 20. Use truth tables to establish the truth of each statement in 24-27. 21 A conditional lut to its "No might j thing an The E thing sente betw tion If state P→ then F of the truth 29. 30. 31. Re tw 37
Transcribed Image Text:ot contain → 9 2.2.3, llow- real uiv- your ally to JS. u s no12 If it walks like a duck and it talks like a duck, then it is a duck. Either it does not walk like a duck or it does not talk like a duck, or it is a duck. If it does not walk like a duck and it does not talk like a duck, then it is not a duck. 19. True or false? The negation of "If Sue is Luiz's mother, then Ali is his cousin" is "If Sue is Luiz's mother, then Ali is not his cousin." years old. 20. Write negations for each of the following statements. (Assume that all variables represent fixed quantities or enti- ties, as appropriate.) a. If P is a square, then P is a rectangle. b. If today is New Year's Eve, then tomorrow is January. c. If the decimal expansion of r is terminating, then r is rational. d. If n is prime, then n is odd or n is 2. e. If x is nonnegative, then x is positive or x is 0. f. If Tom is Ann's father, then Jim is her uncle and Sue is her aunt. g. If n is divisible by 6, then n is divisible by 2 and n is divisible by 3. 21. Suppose that p and q are statements so that p →q is false. Find the truth values of each of the following: a.~p q b. pvq c. q→ P H 22. Write contrapositives for the statements of exercise 20. H 23. Write the converse and inverse for each statement of exercise 20. Use truth tables to establish the truth of each statement in 24-27. 21 A conditional lut to its "No might j thing an The E thing sente betw tion If state P→ then F of the truth 29. 30. 31. Re tw 37
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