Let mathrm{A}, mathrm{B}, mathrm{C} and mathrm{D} be four non-empty sets. contrapositive statement o

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Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ be four non-empty sets. The contrapositive statement of "If $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D},$ then $\mathrm{A} \subseteq \mathrm{C}^{\prime \prime}$ is

If $\mathrm{A} \subseteq \mathrm{C},$ then $\mathrm{B} \subset \mathrm{A}$ or $\mathrm{D} \subset \mathrm{B}$

If $\mathrm{A} \ne \mathrm{C},$ then $\mathrm{A} \neq \mathrm{B}$ or $\mathrm{B} \ne \mathrm{D}$

If $\mathrm{A}\ne\mathrm{C},$ then $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D}$

If $\mathrm{A} \neq \mathrm{C},$ then $\mathrm{A} \neq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D}$

(JEE MAIN-2020)

Contrapositive of $\mathrm{p} \rightarrow \mathrm{q}$ is $\sim \mathrm{q} \rightarrow \sim \mathrm{p}$

$(\mathrm{A} \subseteq \mathrm{B}) \Lambda(\mathrm{B} \subseteq \mathrm{D}) \longrightarrow(\mathrm{A} \subseteq \mathrm{C})$

Contrapositive is

$\sim(\mathrm{A} \subseteq \mathrm{C}) \longrightarrow \sim(\mathrm{A} \subseteq \mathrm{B}) \vee \sim(\mathrm{B} \subseteq \mathrm{D})$

$\mathrm{A} \neq \mathrm{C} \rightarrow(\mathrm{A} \neq \mathrm{B}) \vee(\mathrm{B} \neq \mathrm{D})$

Standard 11

Mathematics