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 numbers,s

Vedclass · Accepted Answer

{ $x : x$ 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 whose square is $-1$. Thus,this set contains no elements and is the empty set.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 $\{2, -1\}$.Therefore,the correct option is $B$.

Similar Questions

If $A$ and $B$ are sets,then $A \cap (B - A)$ is

If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$,then:

The set $A = \{ x: x \in R, x^2 = 16 \text{ and } 2x = 6 \}$ equals

If $X = \{ 4^n - 3n - 1 : n \in N \}$ and $Y = \{ 9(n - 1) : n \in N \}$,then $X \cup Y$ = . . . . .

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if:

Vedclass Test Series

Exam Paper Generator

Online Exam Module