Show that $A \cap B = A \cap C$ does not necessarily imply $B = C$.
(N/A) Let $A = \{0, 1\}, B = \{0, 2, 3\},$ and $C = \{0, 4, 5\}$.
Accordingly,$A \cap B = \{0\}$ and $A \cap C = \{0\}$.
Here,$A \cap B = A \cap C = \{0\}$.
However,$B \neq C$ because $2 \in B$ and $2 \notin C$.
Accordingly,$A \cap B = \{0\}$ and $A \cap C = \{0\}$.
Here,$A \cap B = A \cap C = \{0\}$.
However,$B \neq C$ because $2 \in B$ and $2 \notin C$.
Explore More
Similar Questions
Are the following pair of sets equal? Give reasons.
$A = \{ x : x \text{ is a letter in the word } \text{FOLLOW} \}$
$B = \{ y : y \text{ is a letter in the word } \text{WOLF} \}$
$A = \{ x : x \text{ is a letter in the word } \text{FOLLOW} \}$
$B = \{ y : y \text{ is a letter in the word } \text{WOLF} \}$
Easy
View SolutionWrite the solution set of the equation $x^2 + x - 2 = 0$ in roster form.
Easy
View SolutionIf $A = \{1, 2, 3, \ldots, 10\}$,then the number of non-empty subsets of $A$ containing only odd numbers is
List all the subsets of the set $\{-1, 0, 1\}$.
Easy
View SolutionIs it true that for any sets $A$ and $B$,$P(A) \cup P(B) = P(A \cup B)$? Justify your answer.
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