Question

The interval notation of the set {: ∈ , −23 < 100} is

(A) [−4, ∞) (B) (0,4] (C) (−∞, 4] (D) (−∞,∞)​

Answer 1

Answer:

Let C be a collection of sets. Then the union of C is

[

C = {x : x ∈ X for some X ∈ C} ,

and the intersection of C is

\

C = {x : x ∈ X for every X ∈ C} .

If C = {A, B}, then this definition reduces to our previous one for A ∪ B and

A ∩ B.

The Cartesian product X × Y of sets X, Y is the set of all ordered pairs (x, y)

with x ∈ X and y ∈ Y . If X = Y , we often write X × X = X2

. Two ordered

pairs (x1, y1), (x2, y2) in X × Y are equal if and only if x1 = x2 and y1 = y2. Thus,

(x, y) 6= (y, x) unless x = y. This contrasts with sets where {x, y} = {y, x}.