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
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Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

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

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

✴➡️(i) For X = {1, 2, 3, 4, 5, 6}, it is 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

➡️Therefore, 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}

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Answer 2

Answer:

✴➡️(i) For X = {1, 2, 3, 4, 5, 6}, it is 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

➡️Therefore, 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}✔

Step-by-step explanation:

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