List all the elements of each of the sets given below.

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}

 

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