Let Q(x, y) be the statement “x has sent an e-mail message

Chapter 7, Problem 3E

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QUESTION:

Let \(Q(x, y)\) be the statement " \(x\) has sent an e-mail message to \(y\), "where the domain for both \(x\) and \(y\) consists of all students in your class. Express each of these quantifications in English.

a) \(\exists x \exists y Q(x, y)\)

b) \(\exists x \forall y Q(x, y)\)

c) \(\forall x \exists y Q(x, y)\)

d) \(\exists y \forall x Q(x, y)\)

e) \(\forall y \exists x Q(x, y)\)

f) \(\forall x \forall y Q(x, y)\)

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QUESTION:

Let \(Q(x, y)\) be the statement " \(x\) has sent an e-mail message to \(y\), "where the domain for both \(x\) and \(y\) consists of all students in your class. Express each of these quantifications in English.

a) \(\exists x \exists y Q(x, y)\)

b) \(\exists x \forall y Q(x, y)\)

c) \(\forall x \exists y Q(x, y)\)

d) \(\exists y \forall x Q(x, y)\)

e) \(\forall y \exists x Q(x, y)\)

f) \(\forall x \forall y Q(x, y)\)

ANSWER:

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Given that

Assume  Q(x, y) be a given statement where

“x has sent an e-mail message to y,” and the domain for both x and y consists of all students in  class.

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