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:

∀

michael scott & dwight schrute

step-by-step explanation:

lazy scranton music video

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3