Answered: Determine whether the statement, given…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 33E: Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that...

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Determine whether the statement, given in inverted commas" is trueor false. If the statement is false, make the necessary change(s) to produce a true statement:

"Some rational numbers are not positive."

Expert Solution

Step 1 Let us find the statement is true or false

$R a t i o n a l n u m b e r s : A l l n u m b e r s i n t h e f o r m o f \frac{p}{q} W h e r e b o t h p a n d q a r e i n t e g e r s, q \neq 0 " S o m e r a t i o n a l n u m b e r s a r e n o t p o s i t i v e " T R U E E x a m p l e : - 2 i s a r a t i o n a l n u m b e r \frac{- 2}{1} = \frac{p}{q} f o r m q \neq 0 a n d a l s o n e g a t i v e v a l u e W e c a n g i v e l o t s o f e x a m p l e t o t h e s t a t e m e n t . S o m e r a t i o n a l n u m b e r s a r e n o t p o s i t i v e = T r u e B u t a l l r a t i o n a l n u m b e r s a r e n o t p o s i t i v e$

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