Question

Rewrite each of the following statements in the form "∀ _____ x, _____."

Answer 1

Answer:

The rewritten statements is as follows:

(a) ∀ dinosaur x, x is extinct.

(b) ∀ real $number$ x, x is positive, $negative$, or zero.

(c) ∀ irrational $number$ x, x is not an $integer$.

(d) ∀ logician x, x is not lazy.

(e) ∀ integer x, $x^2 \ne 2,147,581,953$

(f)  ∀ real number x, $x^2 \ne -1$

Step-by-step explanation:

As a general rule, words like "all", "every", "the", etc. are represented with ∀.

However, some sentences may be need to rephrased before such sentence can be rephrased

So, the following replacement will be made:

(a)

$All \to$ ∀

$dinosaurs \to x$

(b)

$Every \to$ ∀

$real\ number \to x$

(c)

First, we need to rephrase this sentence to:

Every irrational number is not integer

So, the replacement is:

$Every \to$ ∀

$irrational\ number \to x$

(d)

First, we need to rephrase this sentence to:

Every logician is lazy

So, the replacement is:

$Every \to$ ∀

$lazy \to x$

(e)

First, we need to rephrase this sentence to:

The integer 2,147,581,953...............

So, the replacement is:

$The \to$ ∀

$Integer \to x$

(f)  

Replace:

$The \to$ ∀

$-1 \to x^2$