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Math / Discrete Mathematics and Its Applications 7 / Chapter 1.SE / Problem 29E

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Let P(x) and Q(x) be prepositional functions. Show always

Chapter 1, Problem 29E

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QUESTION:

Let $P(x)$ and $Q(x)$ be propositional functions. Show that $\exists x(P(x) \rightarrow Q(x))$ and $\forall x P(x) \rightarrow \exists x Q(x)$ always have the same truth value.

Equation Transcription:

$P(x)$

$Q(x)$

$∃x\ (P(x)\ →\ Q(x))$

$∀x\ P(x)\ →\ ∃x\ Q(x)$

$x$

$x\ ≥\ 0$

$\sqrt{\ }x\$ i

Text Transcription:

P(x)

Q(x)

Exists x (P(x) right arrow Q(x))

x P(x) right arrow Exists x Q(x)

Questions & Answers

QUESTION:

Let $P(x)$ and $Q(x)$ be propositional functions. Show that $\exists x(P(x) \rightarrow Q(x))$ and $\forall x P(x) \rightarrow \exists x Q(x)$ always have the same truth value.

Equation Transcription:

$P(x)$

$Q(x)$

$∃x\ (P(x)\ →\ Q(x))$

$∀x\ P(x)\ →\ ∃x\ Q(x)$

$x$

$x\ ≥\ 0$

$\sqrt{\ }x\$ i

Text Transcription:

P(x)

Q(x)

Exists x (P(x) right arrow Q(x))

x P(x) right arrow Exists x Q(x)

ANSWER:

Solution

Step 1:

Let P(x) and Q(x) be propositional functions.

We have to show that $\exists{}x(P(x)\rightarrow{}Q(x))$ and $\forall{}xP(x)\rightarrow{}\exists{}xQ(x)$ always the same truth value.

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Solution Found!

Let P(x) and Q(x) be prepositional functions. Show always

Questions & Answers

Study Tools You Might Need

Chapter: 2 Problem: 40

Chapter: 1 Problem: 1.6

Chapter: 5 Problem: 14

Chapter: 7 Problem: 4

Chapter: 22 Problem: 84

Chapter: 14 Problem: 2

Chapter: 3 Problem: 1

Chapter: 34 Problem: 1

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Solution Found!

Let P(x) and Q(x) be prepositional functions. Show always

Questions & Answers

Study Tools You Might Need

Chapter: 2 Problem: 40

Chapter: 1 Problem: 1.6

Chapter: 5 Problem: 14

Chapter: 7 Problem: 4

Chapter: 22 Problem: 84

Chapter: 14 Problem: 2

Chapter: 3 Problem: 1

Chapter: 34 Problem: 1

Not The Solution You Need? Search for Your Answer Here:

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