If this is a theorem, derive it inpropositional logic. If it is not, show that it is notusing a tree. If you use TI, prove the theorem,independently.F^(M <> N) > *((M & N) v (*M & ~N))

Name: If this is a theorem, derive it inpropositional logic. If it is not,
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Description: If this is a theorem, derive it inpropositional logic. If it is not, show that it is notusing a tree. If you use TI, prove the theorem,independently.F^(M <> N) > *((M & N) v (*M & ~N))

Answered: If this is a theorem, derive it in…

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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If this is a theorem, derive it in
propositional logic. If it is not, show that it is not
using a tree. If you use TI, prove the theorem,
independently.
F^(M <> N) > *((M & N) v (*M & ~N))

Expert Solution

Step 1

Given- ~(M ↔ N) → ~((M & N) v (~M & ~N)

To prove it by propositional logic

Step 2 ~(M ↔ N)

$w e n e e d t o p r o v e t h e g i v e n t h e o r e m i m p r e p o s i t i o n a l l o g i c . T r u t h t a b l e o f ~ (M \leftrightarrow N) i s a s f o l l o w :$

M	N	$M \leftrightarrow N$	$~ (M \leftrightarrow N)$
True	True	True	False
True	False	False	True
False	True	False	True
False	False	True	False

Table-1

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