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माना $A , B , C$ तथा $D$ चार अरिक्त समुच्चय हैं तो कथन "यदि $A \subseteq B$ तथा $B \subseteq D$, तो $A \subseteq C ^{\prime \prime}$ का प्रतिधनात्मक कथन है
यदि $A \subseteq C$, तो $B \subset A$ अथवा $D \subset B$
यदि $A \not \subseteq C$, then $A \not \subseteq B$ अथवा $B \not \subseteq D$
यदि $A \nsubseteq \subseteq C$, then $A \subseteq B$ तथा $B \subseteq D$
यदि $A \nsubseteq \subseteq C$, then $A \not \subseteq B$ तथा $B \subseteq D$
Solution
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
$\sim(\mathrm{A} \subseteq \mathrm{C}) \longrightarrow \sim(\mathrm{A} \subseteq \mathrm{B}) \vee \sim(\mathrm{B} \subseteq \mathrm{D})$
$\mathrm{A} \neq \mathrm{C} \rightarrow(\mathrm{A} \neq \mathrm{B}) \vee(\mathrm{B} \neq \mathrm{D})$
