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Rewrite each of the following statements in the form "∀ _____ x, _____."
(a) All dinosaurs are extinct. ∀ ---Select--- x, ---Select--- .
(b) Every real number is positive, negative, or zero. ∀ ---Select--- x, ---Select--- .
(c) No irrational numbers are integers. ∀ ---Select--- x, ---Select--- .
(d) No logicians are lazy. ∀ ---Select--- x, ---Select--- .
(e) The number 2,147,581,953 is not equal to the square of any integer. ∀ ---Select--- x, ---Select--- .
(f) The number −1 is not equal to the square of any real number.

Sagot :

MrRoyalidn

Answer:

The rewritten statements is as follows:

(a) ∀ dinosaur x, x is extinct.

(b) ∀ real [tex]number[/tex] x, x is positive, [tex]negative[/tex], or zero.

(c) ∀ irrational [tex]number[/tex] x, x is not an [tex]integer[/tex].

(d) ∀ logician x, x is not lazy.

(e) ∀ integer x, [tex]x^2 \ne 2,147,581,953[/tex]

(f)  ∀ real number x, [tex]x^2 \ne -1[/tex]

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)

[tex]All \to[/tex] ∀

[tex]dinosaurs \to x[/tex]

(b)

[tex]Every \to[/tex] ∀

[tex]real\ number \to x[/tex]

(c)

First, we need to rephrase this sentence to:

Every irrational number is not integer

So, the replacement is:

[tex]Every \to[/tex] ∀

[tex]irrational\ number \to x[/tex]

(d)

First, we need to rephrase this sentence to:

Every logician is lazy

So, the replacement is:

[tex]Every \to[/tex] ∀

[tex]lazy \to x[/tex]

(e)

First, we need to rephrase this sentence to:

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

So, the replacement is:

[tex]The \to[/tex] ∀

[tex]Integer \to x[/tex]

(f)  

Replace:

[tex]The \to[/tex] ∀

[tex]-1 \to x^2[/tex]

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