The roster form
1. Express the following sets using the roster form:
(a) {x ∈ N | 25 ≤ x2 < 50}
(b) {x ∈ Z | 25 ≤ x2 < 50} Hint: This set is different than (a).
(c) {3n : n ∈ Z and − 1 ≤ n ≤ 2}
(d) {3n ∈ Z : −1 ≤ n ≤ 2} Hint: This set is different than (c).
2. Use set builder notation to give a description of the set {−10, −5, 0, 5, 10, 15}.
3. List the members, i.e. elements, of the following sets.
(a) {x, {y}, {x, y}}
(b) P({x, {y}, {x, y}})
4. Let A = {1, 2, 5, 6, 7} and B = {2, 3, 4, 7, 8}. Find the following sets.
(a) A ∩ B
(b) A ∪ B
(c) A − B
(d) B − A
(e) A under the assumption that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
5. Use Venn diagrams to verify the identity A ⊕ B = (A ∪ B) − (A ∩ B). Moreover, clearly
identify each region of the identity in your responses. That is, don’t just identify the final regions
of the left and right hand sides; show how the final region is formed.
6. Let A = {1, 2, 3, 4} × {1, 2, 3}.
(a) What is the cardinality of A?
(b) Define the subset B of A as B = {(s, t) ∈ A : s ≤ t}. List the elements of B.
regards to the osmosis of pieces into lumps. Mill operator recognizes pieces and lumps of data, the differentiation being that a piece is comprised of various pieces of data. It is fascinating regards to the osmosis of pieces into lumps. Mill operator recognizes pieces and lumps of data, the differentiation being that a piece is comprised of various pieces of data. It is fascinating to take note of that while there is a limited ability to recall lumps of data, how much pieces in every one of those lumps can change broadly (Miller, 1956). Anyway it's anything but a straightforward instance of having the memorable option huge pieces right away, somewhat that as each piece turns out to be more natural, it very well may be acclimatized into a lump, which is then recollected itself. Recoding is the interaction by which individual pieces are 'recoded' and allocated to lumps. Consequently the ends that can be drawn from Miller's unique work is that, while there is an acknowledged breaking point to the quantity of pi