Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
${1, 2, 3} \subset A$
${1, 2, 3} \subset A$
(A) Given the set $A = \{1, 2, \{3, 4\}, 5\}$.
The statement $\{1, 2, 3\} \subset A$ is incorrect.
Reason: For a set to be a subset of $A$,every element of the set must be an element of $A$.
In the set $\{1, 2, 3\}$,the elements are $1, 2,$ and $3$.
While $1 \in A$ and $2 \in A$,the element $3$ is not an element of $A$ (only the set $\{3, 4\}$ is an element of $A$).
Therefore,$\{1, 2, 3\} \not\subset A$.
The statement $\{1, 2, 3\} \subset A$ is incorrect.
Reason: For a set to be a subset of $A$,every element of the set must be an element of $A$.
In the set $\{1, 2, 3\}$,the elements are $1, 2,$ and $3$.
While $1 \in A$ and $2 \in A$,the element $3$ is not an element of $A$ (only the set $\{3, 4\}$ is an element of $A$).
Therefore,$\{1, 2, 3\} \not\subset A$.
Explore More
Similar Questions
Let $A, B, C$ be subsets of a set $X$. Which of the following set-theoretic statements is valid?
Which of the following is an example of the null set?
$\{ x : x \in \mathbb{N}, x < 5 \text{ and } x > 7 \}$
$\{ x : x \in \mathbb{N}, x < 5 \text{ and } x > 7 \}$
Easy
View SolutionIf $aN = \{ax : x \in N\}$ and $bN \cap cN = dN$,where $b, c \in N$ are coprime numbers,then:
Medium
View SolutionLet $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
$\{\varnothing\} \subset A$
$\{\varnothing\} \subset A$
Easy
View SolutionWrite the solution set of the equation $x^2 + x - 2 = 0$ in roster form.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo