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

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)