3. (i) Let A = (a, b) be an arbitrary open interval. Write A as a countable union or a countable intersection of half‐open intervals. (ii) Let B = (a, b] be an arbitrary half‐open interval. Write B as a countable union or a countable intersection of open intervals.

Q: 3.Determine the intersection X ∩ Y. Express the  in interval notation. X = {x/ x>equal 8} and Y =…

A: We have: X=x  x≥8=[8,∞)Y=x  x<7=(-∞,7)

Q: Let W = (-∞,∞) be the universal set and Q = [-3,7) and P = [-5,4]. In interval notation, determine…

A:

Q: write as interval the set defined on the real line 45 67 8 -3 -2 -1 0 1 2 a) b) -2 c) -5 -4 -3 -2 -1…

A: It is known that, while writing the interval we have to decide that whether the interval is open or…

Q: An interval a ≤ x ≤ b means that the endpoints a and b are not regarded as points belonging to the…

A:

Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: Use graphs to find set. (-3, 0)∩[-1, 2]

A: The given sets are We need to find the intersection of these two sets using graphs.

Q: The set {[1 -1 3], [2 3 -2], [3 2 1], [0 0 0]} spans صواب İhi

A:

Q: For Exercise, write the set as a single interval. [(-0, 6) U (10, o)] N [8, 12)

A: We will draw them on a number line. Draw:

Q: Which of the following relations contain cach of the following pairs (1, 1), (1, 2), (3, 2), and…

A:

Q: {(r.0):3<rs4 and so<- Neatly sketch the set of points

A:

Q: For each part, write the set in the form [x | P(x)] (property that describes the elements of the…

A: Explained below

Q: Use graphs to find the set : (- ∞, 5) ∪ [1, 8)

A: Given that -∞,5∪[1,8). First draw the graph of -∞,5 and [1,8).

Q: Graph each set of numbers given in interval notation. Then write an inequality statement in x…

A:

Q: B. Write each solution set in interva 1. x 1 2. x 8 3. -2 < x < 6 4. -7 < x S-1 <x < 0 5. 2

A:

Q: The maximal interval?

A: Given D.E is    with initial condition   .And solution is

Q: Determine the intersection X ∩ Y. Express the in interval notation. X = {x/ x>equal 8} and Y =…

A:

Q: Let A={1,2,3,5,9}, B={0,6,7,8,10}. Determine (A∖B)∪(B∖A)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: Introduction: The number of elements carried by the operation and executing the results of a…

Q: -5 -4 -3 -2 -1 0 1 2 4 or -5 4 -3 -2 -1 0 1 2 3 45 Answer (b): number line, write the set in…

A: A detailed solution is given below.

Q: Graph the set and write the interval notation : a) (-00, -1]U (-3, 12] b) [0, 8) n (3, 12]

A:

Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.