Express the following set in roster form: H = { x : x ∈ W and x < 10 }

We are given to express the following set in roster form: H = { x : x ∈ W and x < 10 } The steps of writing a set in roster form are: (i) Identify all elements of the set (ii) List the elements within a pair of curly braces, separated by commas. Here, x ∈ W ⇒ the element is a whole number and x < 10 means the element is less than 10 . We know that the whole numbers less than 10 are 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 . So, the elements of the set are 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 . Therefore, the roster form of the given set is H = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 .

Express the following set in roster form: J = { x : x ∈ N and 2 x - 3 ≤ 17 }

We are given to express the following set in roster form: J = { x : x ∈ N and 2 x - 3 ≤ 17 } The steps of writing a set in roster form are: (i) Identify all elements of the set (ii) List the elements within a pair of curly braces, separated by commas. Now, 2 x - 3 ≤ 17 ⇒ 2 x - 3 + 3 ≤ 17 + 3 [Add 3 to both the sides] ⇒ 2 x ≤ 20 ⇒ 2 x 2 ≤ 20 2 [Divide both the sides by 2 ] ⇒ x ≤ 10 So, the elements of the required set will be a natural number less than or equal to 10 . We know that the natural numbers equal to or less than 10 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 and 10 . So, the elements of the set are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 and 10 . Therefore, the roster form of the given set is J = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 .