Question

Write the set {x : x n and x2 < 25} in roster form

Answer 1

Answer:

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First thing analyze the given data. x ϵ N that implies x is a natural number.

x2 < 25

⇒ x < ±5

As x belongs to the natural number that means x < 5.

All numbers less than 5 are 1,2,3,4.

∴ Roster form will be {1,2,3,4}.

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Answer 2

The roster form of the set {x : x ∈ n and x² < 25}  is { 1, 2, 3, 4 }.

Given: The set {x : x ∈ n and x² < 25}

To Find: The set {x : x ∈ n and x² < 25} in roster form.

Solution:  

• The set given in the question is in set-builder form which is a descriptive form and states the properties of the elements of the set.
• The roster form is a way of describing a set in which the elements are directly listed inside a pair of curly brackets and are separated by commas.

The question says,  {x : x ∈ n and x² < 25} which means we need to take those natural numbers whose squares are less than 25.

As natural number start from 1, so we check from 1 itself.

            1² = 1       [ which is less than 25 ]

            2² = 4     [ which is less than 25 ]

            3² = 9    [ which is less than 25 ]

            4² = 16    [ which is less than 25 ]

            5² = 25   [ which is not less than 25 ]

Thus the set must include = { 1, 2, 3, 4 }

Hence, the roster form of the set {x : x ∈ n and x² < 25}  is { 1, 2, 3, 4 }.

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