Question

Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:

(i) n ∈ X but 2n ∉ X

(ii) n + 5 = 8

(iii) n is greater than 4​

Answer 1

(i) For the value of X = {1, 2, 3, 4, 5, 6}, it is given to us that n ∈ X, here 2n ∉ X.

Let, A = {x | x ∈ X and 2x ∉ X}

Here, 1 ∉ A is taken as 2.1 = 2 ∈ X

2 ∉ A is taken as 2.2 = 4 ∈ X

3 ∉ A is taken as 2.3 = 6 ∈ X

But 4 ∈ A is taken as 2.4 = 8 ∉ X

5 ∈ A is taken as 2.5 = 10 ∉ X

6 ∈ A is taken as 2.6 = 12 ∉ X

We can conclude that, A = {4, 5, 6}

(ii) Let us assume B = {x | x ∈ X and x + 5 = 8}

Then, B = {3} as x = 3 ∈ X and 3 + 5 = 8 and there is no other element in this set which belongs to X such that x + 5 = 8.

(iii) Let us assume C = {x | x ∈ X, x > 4}

Hence, c = {5,6}

Answer 2

Answer:

,

Step-by-step explanation:

For X = {1, 2, 3, 4, 5, 6},it is the given that n ∈ X, but 2n ∉ X.

Let, A = {x | x ∈ X and 2x ∉ X} Now, 1 ∉ A as 2.1 = 2 ∈ X 2 ∉ A

as 2.2 = 4 ∈ X 3 ∉ A as 2.3 = 6 ∈ X

But 4 ∈ A as 2.4 = 8 ∉ X 5 ∈ A

as 2.5 = 10 ∉ X 6 ∈ A as 2.6 = 12 ∉ X

So, A = {4, 5, 6}

(ii) Let B = {x | x ∈ X and x + 5 = 8}

Here, B = {3} as x = 3 ∈ X and 3 + 5 = 8 and there is no other element belonging to X such that x + 5 = 8.

(iii) Let C = {x | x ∈ X, x > 4}

Therefore, C = {5, 6}.