Let U = {a, b, c, e, d, e, f, g, h, i, j, k}; A = {a, b, e, f, h, j}; B = {b, c, d, f, j}. Draw a Venn Diagram with a rectangle for the Universal set given. Label and mark elements for set A and set B.

The rectangle represents the universal set (marked as "set U"). Everything is contained in this rectangle.

Circle A represents set A = {a, b, e, f, h, j}

Circle B represents set B = {b, c, d, f, j}

The common elements between the two sets are {b, f, j}, so we'll write these three values in the overlapping portion of the two circles.

The items {a,e,h} will go in circle A, but not in the overlapping portion since they are found only in set A.

Similarly we'll have {c,d} go in circle B but not in the overlapping portion since these items are only found in set B.

The remaining terms {g, i, k} go outside both circles, but inside the rectangle, because neither of these elements are in set A or set B.

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true