Which of the following is the empty set?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The empty set is a set that contains no elements.For option $A$: $x^2 - 1 = 0$ $\Rightarrow x^2 = 1$ $\Rightarrow x = \pm 1$. These are real numbe

Vedclass · Accepted Answer

$ \{ x : x 	ext{ is a real number and } x^2 + 1 = 0 \} $

Vedclass · Answer

(B) The empty set is a set that contains no elements.For option $A$: $x^2 - 1 = 0$ $\Rightarrow x^2 = 1$ $\Rightarrow x = \pm 1$. These are real numbers,so the set is $\{ -1, 1 \}$.For option $B$: $x^2 + 1 = 0 \Rightarrow x^2 = -1$. There is no real number $x$ such that its square is negative. Thus,this set is empty.For option $C$: $x^2 - 9 = 0$ $\Rightarrow x^2 = 9$ $\Rightarrow x = \pm 3$. These are real numbers,so the set is $\{ -3, 3 \}$.For option $D$: $x^2 - x - 2 = 0$ $\Rightarrow (x - 2)(x + 1) = 0$ $\Rightarrow x = 2, -1$. These are real numbers,so the set is $\{ -1, 2 \}$.Therefore,the correct option is $B$.

Similar Questions

State which of the following sets are finite or infinite:
$\{ x : x \in N \text{ and } x \text{ is odd} \}$

If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then find $n(C)$.

If $A = \{1, 2, 3, 4, 5\}$,then the number of proper subsets of $A$ is

Write the following set in roster form:
$C = \{ x : x \text{ is a two-digit natural number such that the sum of its digits is } 8 \}$

Which of the following pairs of sets are disjoint?
$A = \{ x : x \text{ is an even integer} \}$
$B = \{ x : x \text{ is an odd integer} \}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module