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
If $A = \{x \in \mathbb{R} : x^2 + 5|x| + 6 = 0\}$,then $n(A) = $
Let $A = \{a, e, i, o, u\}$ and $B = \{a, b, c, d\}$. Is $A$ a subset of $B$? No. (Why?). Is $B$ a subset of $A$? No. (Why?)
Easy
View SolutionConsider the sets $\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $A, \ldots B$.
Easy
View SolutionLet $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)
Medium
View SolutionThe set $A = \{ x : x \in \mathbb{R}, x^2 = 16 \text{ and } 2x = 6 \}$ is equal to
Medium
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