Find a domain for the quantifiers in such that this

ISBN: 9780073383095 37

Solution for problem 23E Chapter 1.SE

Discrete Mathematics and Its Applications | 7th Edition

Discrete Mathematics and Its Applications | 7th Edition

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Problem 23E

Find a domain for the quantifiers in $\exists x \exists y(x \neq y \wedge$ $\forall z((z=x) \vee(z=y)))$ such that this statement is false.

Equation Transcription:

$\neg{}(p\rightarrow{}(q\wedge{}\ r))$

$p\ \vee{}\neg{}q$

$\neg{}r$

$(p\ \wedge{}r)\vee{}(q\rightarrow{}p)$

Text Transcription:

Neg (p right arrow (q wedge r))

P vee q

Neg r

(p wedge r) vee (q right arrow p)

Step-by-Step Solution:

Solution:

Step 1 :

we have to find a domain for a quantifiers in $\exists{}x\exists{}y(x\ne{}y\wedge{}\forall{}z((z=x\vee{}z=y)))$

this means there exist x and there exist y and also shows that x is not equal to y

and for all z obeys z is either equal to x or equal to y.

.’. The domains are

x=all add numbers

y=all even number and

z=real number or natural number.

Step 2 of 1

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