Which of the following sets is a universal set for the other four sets? (a) The set of even natural numbers

(b) The set of odd natural numbers

(c) The set of natural numbers

(d) The set of negative numbers

(e) The set of integers

The set of integers is a universal set for the other four sets ⇒ (e)

Step-by-step explanation:

The set of even natural numbers is {2, 4, 6, 8, 10, 12, }

The set of odd natural numbers is {1, 3, 5, 7, 9, 11, 13, }

The set of natural numbers is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, }

The set of negative numbers is {-1, -2, -3, -4, -5, -6, }

The set of integers is {, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, }

∵ The set of integers contains all even natural numbers, all the odd

   natural numbers

∴ It contains all the natural numbers

∵ The set of integers contains all the negative numbers

∴ The set of integers contains the other four sets

∴ The set of integers is a universal set for the other four sets

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.