 # If Y = {1, 2, 3,…, 10}, and a represents any element of Y, `
Question:

If Y = {1, 2, 3,…, 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

(i) a ∈ Y but a2∉ Y

(ii) a + 1 = 6, a ∈ Y

(iii) a is less than 6 and a ∈ Y

Solution:

(i) According to the question,

Y = {1, 2, 3,…, 10} where a represents any element of Y

Y = {1, 2, 3,…, 10}

12 = 1, 22 = 4, 32 = 9

1, 4, 9 ∈ Y ⇒ 1, 2, 3 do not satisfy given condition

Hence,

{a: a ∈ Y and a2∉ Y} = {4, 5, 6, 7, 8, 9, 10}

(ii) According to the question,

Y = {1, 2, 3,…, 10} where a represents any element of Y

Y = {1, 2, 3,…, 10}

a + 1 = 6 ⇒ a = 5

⇒ 5 satisfies the given condition

Hence,

{a: a + 1 = 6, a ∈ Y } = {5}

(iii) According to the question,

Y = {1, 2, 3,…, 10} where a represents any element of Y

Y = {1, 2, 3,…, 10}

a is less than 6 ⇒ 1, 2, 3, 4, 5

1, 2, 3, 4, 5 satisfy the given condition

Hence,

{a: a is less than 6, a ∈ Y } = {1, 2, 3, 4, 5}