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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
How do you do number 20. Questions a,b, c, d and those statements contrapositives?
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
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"No
might j
thing an
The E
thing
sente
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If state
P→
then F
of the
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29.
30.
31.
Re
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37
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