Answered: Advanced Math Question

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

Expert Solution

Step 1

The objective is to negate each given statement and check whether the negation is true.

For a:

Consider the given statement

p: some bears are brown.

negation of this statement is:

$~ p : n o b e a r i s b r o w n . B u t t h e r e a r e s o m e b e a r s t h a t a r e b r o w n, t h u s ~ p i s F a l s e . T h u s, n e g a t i o n o f f i r s t s t a t e m e n t s i s f a l s e .$

Step 2

For b:

Consider the given statement

q: All integers are positive.

negation of this statement is:

$~ q : S o m e i n t e g e r s a r e n o t p o s i t i v e . A n d t h i s i s t r u e t h a t t h e r e a r e s o m e i n t e g e r s t h a t a r e n o t p o s i t i v e f o r e x a m p l e - 2 . T h u s ~ q i s t r u e . T h u s, n e g a t i o n o f s e c o n d s t a t e m e n t s i s t r u e .$