Show that if $A \subset B$,then $(C - B) \subset (C - A)$.
(N/A) Let $A \subset B$.
To show: $(C - B) \subset (C - A)$.
Let $x \in (C - B)$.
$\Rightarrow x \in C$ and $x \notin B$.
Since $A \subset B$,if $x \notin B$,then $x \notin A$.
$\Rightarrow x \in C$ and $x \notin A$.
$\Rightarrow x \in (C - A)$.
Therefore,$(C - B) \subset (C - A)$.
To show: $(C - B) \subset (C - A)$.
Let $x \in (C - B)$.
$\Rightarrow x \in C$ and $x \notin B$.
Since $A \subset B$,if $x \notin B$,then $x \notin A$.
$\Rightarrow x \in C$ and $x \notin A$.
$\Rightarrow x \in (C - A)$.
Therefore,$(C - B) \subset (C - A)$.
Explore More
Similar Questions
Examine whether the following statement is true or false:
$\{a\} \in \{a, b, c\}$
$\{a\} \in \{a, b, c\}$
Easy
View SolutionGiven the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all three sets $A$,$B$,and $C$?
Easy
View SolutionIf $A = \{2, 3, 4, 5, 6\}$,then which of the following statements has a truth value of 'false'?
If $A = \{ 1, 2, 3, 4, 5 \}$,then what is the number of proper subsets of $A$?
Easy
View SolutionWrite the set builder form of the set $ A = \{-1, 1\} $.
MediumKCET 2015
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