Which of the following is an empty set?

Question

Question

Answer 1

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.