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.

The rewritten statements is as follows:

(a) ∀ dinosaur x, x is extinct.

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

(c) ∀ irrational x, x is not an .

(d) ∀ logician x, x is not lazy.

(e) ∀ integer x,

(f)  ∀ real number x,

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)

∀

(b)

∀

(c)

First, we need to rephrase this sentence to:

Every irrational number is not integer

So, the replacement is:

∀

(d)

First, we need to rephrase this sentence to:

Every logician is lazy

So, the replacement is:

∀

(e)

First, we need to rephrase this sentence to:

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

So, the replacement is:

∀

(f)  

Replace:

∀

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2