1) Translate the following sentences into logical notation and then negate the statementusing logical rules.a) If a is odd then a² is oddb) The number r is positive, but the number y is not positivec) If x is prime, then Vī is not a rational number.d) For every prime umber p, there is another prime number q with q > pe) For every positive mumber e , there is a positive number ő such that |r – a| < 6 implies\S(x) – S(a)| < e .f) For every positive number e , there is a positive number M for which |f(z) – b| < ewhenever r > M.g) There exists a real number a for which a + x = x for every real number r.h) If sin(x) < 0, then it is not the case that 0 <1< a.i) If f is a polynomial and its degree is greater than 2, then f' is not constant.

Solution for a) let p:a is odd number. q: a2 is odd. Logical notation id p→q its negation is ~p→~q

1) Translate the following sentences into logical notation and then negate the statement using logical rules. a) If a is odd then a² is odd b) The number r is positive, but the mumber y is not positive c) If x is prime, then vī is not a rational number.

1) Translate the following sentences into logical notation and then negate the statement using logical rules. a) If a is odd then a² is odd b) The number r is positive, but the mumber y is not positive c) If x is prime, then vī is not a rational number.

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) Translate the following sentences into logical notation and then negate the statement
using logical rules.
a) If a is odd then a² is odd
b) The number r is positive, but the number y is not positive
c) If x is prime, then Vī is not a rational number.
d) For every prime umber p, there is another prime number q with q > p
e) For every positive mumber e , there is a positive number ő such that |r – a| < 6 implies
\S(x) – S(a)| < e .
f) For every positive number e , there is a positive number M for which |f(z) – b| < e
whenever r > M.
g) There exists a real number a for which a + x = x for every real number r.
h) If sin(x) < 0, then it is not the case that 0 <1< a.
i) If f is a polynomial and its degree is greater than 2, then f' is not constant.

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