If A B, then - Vidyadip

MCQ

If $A \subset B$, then

A
$A^e \subset B^e$
B
$B^e \not \subset A^c$
C
$A^c=B^c$
✓
$B^c \subset A^c$

✓

Answer

Correct option: D.

$B^c \subset A^c$

Let $A \subset$ B
To prove $B^C \subset A^c$, it is enough to show that $x \in B^c \Rightarrow x \in A^c$
$\text { Let } x \in B^C$
$\Rightarrow x \notin B$
$\Rightarrow x \notin A \text { since } A \subset B$
$\Rightarrow x \in A^c$
Hence $B ^{ C } \subset A ^{ C }$

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