Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then

1.	Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then, write the following sets containing all numbers represented by(i) n + 1 (ii) n2
Answer» Given E = {2, 4, 6, 8, 10} (i) Let A = {x \| x = n + 1, n ∈ E} Thus, for 2 ∈ E, x = 3 4 ∈ E, x = 5, and so on. Therefore, A = {3, 5, 7, 9, 11}. (ii) Let B = {x \| x = n², n ∈ E} So, for 2 ∈ E, x = (2)² = 4, 4 ∈ E, x = (4)² = 16, 6 ∈ E, x = (6)² = 36, and so on. Hence, B = {4, 16, 36, 64, 100}

Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then, write the following sets containing all numbers represented by(i) n + 1 (ii) n2

Answer»

Given E = {2, 4, 6, 8, 10}

(i) Let A = {x | x = n + 1, n ∈ E}

Thus, for 2 ∈ E, x = 3

4 ∈ E, x = 5,

and so on. Therefore, A = {3, 5, 7, 9, 11}.

(ii) Let B = {x | x = n², n ∈ E}

So, for 2 ∈ E, x = (2)² = 4, 4 ∈ E, x = (4)² = 16, 6 ∈ E, x = (6)² = 36,

and so on. Hence, B = {4, 16, 36, 64, 100}