Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express th

1.	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» (i) 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}

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»

(i) 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}