Question:
List all the elements of each of the sets given below.
B = {x : x = 2n + 1, n ϵ W and n ≤ 5}.
Solution:
Given: x = 2n + 1 and n ≤ 5
⇒ n = 0, 1, 2, 3, 4 and 5 [∵ n ∈ W]
Given $x=2 n+1$
$n=0, x=2 \times 0+1=1$
$n=1, x=2 \times 1+1=3$
$n=2, x=2 \times 2+1=5$
$n=3, x=2 \times 3+1=7$
$n=4, x=2 \times 4+1=9$
$n=5, x=2 \times 5+1=11$
So, the elements of B are 1, 3, 5, 7, 9 and 11
∴, B = {1, 3, 5, 7, 9, 11}