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If $A$ is a subset of $B$, then which one of the following is correct?
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Verified Answer
The correct answer is:
$B^{c} \subset A^{c}$
Suppose $U=\{a, b, c, d, e, f, g, h\}$ $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\}$
$B=\{a, b, c, d, e\}$ Given $A \subseteq B$
$\mathrm{A}^{\mathrm{c}}=\{\mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\}, \mathrm{B}^{\mathrm{C}}=\{\mathrm{f}, \mathrm{g}, \mathrm{h}\}$
Hence, $\mathrm{B}^{\mathrm{C}} \subseteq \mathrm{A}^{\circ}$
$B=\{a, b, c, d, e\}$ Given $A \subseteq B$
$\mathrm{A}^{\mathrm{c}}=\{\mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\}, \mathrm{B}^{\mathrm{C}}=\{\mathrm{f}, \mathrm{g}, \mathrm{h}\}$
Hence, $\mathrm{B}^{\mathrm{C}} \subseteq \mathrm{A}^{\circ}$
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