Question

3.7.5. Let $P(x)$ be the assertion "$x$ is positive", and let $Q(x)$ the assertion "$x^2 > x$". (a) Is the statement $(forall x in mathbb{R}) [P(x) implies Q(x)]$ true or false? Why? (b) Is the statement $[(forall x in mathbb{R})P(x)] implies [(forall x in mathbb{R})Q(x)]$ true or false? Why?

          3.7.5. Let $P(x)$ be the assertion "$x$ is positive", and let $Q(x)$ the assertion "$x^2 > x$".
(a) Is the statement $(forall x in mathbb{R}) [P(x) implies Q(x)]$ true or false? Why?
(b) Is the statement $[(forall x in mathbb{R})P(x)] implies [(forall x in mathbb{R})Q(x)]$ true or false? Why?

3.7.5. Let P(x) be the assertion "x is positive", and let Q(x) the assertion "x^2 > x".
(a) Is the statement (forall x in mathbbR) [P(x) implies Q(x)] true or false? Why?
(b) Is the statement [(forall x in mathbbR)P(x)] implies [(forall x in mathbbR)Q(x)] true or false? Why?

Added by Soledad M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/05/2023

Step 1

- $ P(x) $ is the assertion "x is positive", which means $ x > 0 $. - $ Q(x) $ is the assertion "$ x^2 > x $", which simplifies to $ x(x - 1) > 0 $. This inequality holds for $ x < 0 $ or $ x > 1 $. Show more…

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