For each of the sets specified below using set-builder notation, use the set-roster method to specify the elements. (a) {n ∈ Z | 20 ≤ n ≤ 35, and n is even} Reminder: Z = {· · · , −3, −2, −1, 0, 1, 2, 3, · · · } is the set of integers. (b) {x ∈ N | 5x < 47, and x is odd} Reminder: N = {1, 2, 3, 4, 5, · · · } is the set of natural numbers. (c) {a ∈ Z | a^2 ≤ 16}

(a) Suppose a, de N. Define what it means to say that d divides a. (b) Find all natural numbers d such that d | 24 but d | 30. (c) Suppose a, b, d E N and that d | a and d | b. Prove that d | a² + b. (d) Suppose X is a non-empty set of real numbers. Define what is meant by an upper bound for X. If X has an upper bound, define what is meant by a supremum for X. (e) Let -{n-1: EN}. {" X = Find (with proof) the supremum of X.

What is the set builder notation and interval notation

Let the universal set R, the set of real numbers. Let A = {x = R| 16 } ○ {xЄR|x6 } {xЄR| 1≤ x ≤6 } {x ЄR| 25}