Question

Which of the following is an empty set?
1. {x : x is a rational number and x² - 1 = 0}
2. {x : x is a rational number and x² - 9 = 0}
3. {x : x is a rational number and x² - 4 = 0}
4. {x : x is a rational number and x² + 1 = 0}

Answer 1

Correct Answer - Option 4 : {x : x is a rational number and x² + 1 = 0}

Concept:

A set which does not contain any element is called an empty set and it is denoted by ϕ.

Calculation:

 

Option 1: {x : x is a rational number and x2 - 1 = 0}

 

As we can see that x = ± 1 satisfies the equation x2 - 1 = 0

 

⇒ {x : x is a rational number and x2 - 1 = 0} is not an empty set.

 

Option 2: {x : x is a rational number and x2 - 9 = 0}

 

As we can see that, x = ± 3 satisfies the equation x2 - 9 = 0

 

⇒ {x : x is a rational number and x2 - 9 = 0} is not an empty set

 

Option 3: {x : x is a rational number and x2 - 4 = 0}

 

As we know that, x = ± 2 satisfies the equation x2 - 4 = 0

 

⇒ {x : x is a rational number and x2 - 4 = 0} is not an empty set

 

Option 4: {x : x is a rational number and x2 + 1 = 0}

 

As we know that, x = ± i satisfies the equation x2 + 1 = 0 but x = ± i is not a rational number.

 

⇒  {x : x is a rational number and x2 + 1 = 0} is an empty set.

 

Hence, option 4 is correct.