Solution to 3. Let P(x), Q(x), and R(x) be the statements “x is a professor,” “x is … - Sikademy
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Archangel Macsika

3. Let P(x), Q(x), and R(x) be the statements “x is a professor,” “x is ignorant,” and “x is vain,” respectively. Express each of these statements using quantifiers; logical connectives; and P(x), Q(x), and R(x), where the domain consists of all people a) No professors are ignorant. b) All ignorant people are vain. c) No professors are vain. d) Does (c) follow from (a) and (b)?

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Here's the Solution to this Question

a)

\nexists x P(x)\iff Q(x)


b)

\forall x Q(x)\iff R(x)


c)

\nexists x P(x)\iff R(x)


d) Answer: yes

since

a) : \neg P\implies Q

b) : Q\implies R

then:

c) : \neg P\implies R

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