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
$A^c=B^c$
D
$B^e \subset A^c$

✓

Answer

(d) $B^c \subset A^c$
Explanation: Let A $\subset$ B
To prove $B^C \subset A^c$, it is enough to show that $x \in B^c \Rightarrow x \in A^c$
$\begin{array}{l}\text { Let } x \in B^C \\
\Rightarrow x \notin B \\
\Rightarrow x \notin A \text { since } A \subset B\end{array}$
$\Rightarrow x \in A^c$
Hence $B ^{ C } \subset A ^{ C }$

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