Are all real numbers either rational or irrational?

Yes. All real numbers are either rational or irrational.

Step-by-step explanation:

The set of all irrational numbers is commonly defined as the set of all real numbers that are not rational.

Let denote the set of all real numbers. Let denote the set of all rational numbers.

For any given real number (,) either is rational () or isn't rational (, such that and thus .)

Assume that isn't a rational number. By the definition of rational numbers, since is a real number but not a rational number (,) would be an irrational number.

Therefore, either is rational or is irrational. Every real number would either be rational or irrational.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92