Exercise No.3
1. Write the elements of the following sets using the set rooster notation.
1. 𝐷 = {𝑥 ∈ 𝑍 ∣ −1 < x < 3}
2. 𝐸 = { 𝑥 ∈ 𝑍 + ∣ −1 < 𝑥 < 3 }
3. 𝑉 = { 𝑠 ∈ 𝑍 ∣∣ 𝑠 > 2 𝑜𝑟 𝑠 < 3 }
4. 𝐴 = {𝑥 ∊ 𝑍 − ∣ −5 < 𝑥 < 5}
5. 𝑁 = { 𝑛 ∊ 𝑍 ∣∣ 𝑛 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 6 }
6. 𝑁 = {𝑛 ∊ 𝑍 + ∣ 𝑛 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 6}
7. A = { x | x ∈ N, x is even, and x < 15}
2. Write the following using set builder notation. Use x to represent the elements in a set.
1. M = {-4, -3, -2, -1, 0, 1, 2}
2. P = {13, 17, 19}
3. Let A = {2, 3, 4} and B = {6, 8, 10} and define a relation R from A to B as follows: For all
(x, y)∊ A x B,
𝑦
(x, y) ∊ R means that 𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 (𝑔𝑖𝑣𝑒𝑛 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛)
a.
b.
c.
d.
e.
f.
Write the ordered pairs of A x B
Is 4R6?
Is 4R8?
Is 2R6?
Is (3, 8)∊ R?
Is (2, 10) ∊ R?