Question

*Which of the following set is not an empty set?*

1️⃣ Set of intersecting points of parallel lines
2️⃣ Set of natural numbers smaller than zero
3️⃣ A = {x I x ∈ W, 3 < x < 4}
4️⃣ B = {x I x^2 = 0}​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following set is not an empty set

1. Set of intersecting points of parallel lines

2. Set of natural numbers smaller than zero

3. A = { x I x ∈ W , 3 < x < 4 }

4. B = { x I x² = 0 }

EVALUATION

CHECKING FOR OPTION : 1

Let S = Set of intersecting points of parallel lines

Since parallel lines never intersect

So there is no intersecting point of parallel lines

So the set of intersecting points of parallel lines is empty set

So this option is not correct

CHECKING FOR OPTION : 2

Let T = Set of natural numbers smaller than zero

We know that set of natural numbers is denoted by N and

N = { 1 , 2 , 3 , 4 , 5 , ... }

We see that there is no natural number smaller than zero

So T contains no element

Therefore Set of natural numbers smaller than zero is empty set

So this option is not correct

CHECKING FOR OPTION : 3

A = { x I x ∈ W , 3 < x < 4 }

We know that set of whole numbers is denoted by W and

W = { 0 , 1 , 2 , 3 , 4 , 5 , ... }

Since there is no whole number between 3 & 4

So A is empty set

So this option is not correct

CHECKING FOR OPTION : 4

B = { x I x² = 0 }

x² = 0 gives x = 0

∴ B = { x I x² = 0 } = { 0 }

So the set B contains one element 0

So B is non empty set , more precisely it is a single ton set

So this option is correct

FINAL ANSWER

Hence the correct option is 4. B = { x I x² = 0 }

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