Let A, B, C and D be four non-empty sets. The | vedclass

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(A) The contrapositive of a conditional statement $p \rightarrow q$ is $\sim q \rightarrow \sim p$.Given the statement: "If $A \subseteq B$ and $B \su

Vedclass · Accepted Answer

If $A 
ot\subseteq C,$ then $A 
ot\subseteq B$ or $B 
ot\subseteq D$

Vedclass · Answer

(A) The contrapositive of a conditional statement $p ightarrow q$ is $\sim q ightarrow \sim p$.Given the statement: "If $A \subseteq B$ and $B \subseteq D,$ then $A \subseteq C$."Let $p$ be $(A \subseteq B) \land (B \subseteq D)$ and $q$ be $(A \subseteq C)$.The negation $\sim q$ is $A 
ot\subseteq C$.The negation $\sim p$ is $\sim((A \subseteq B) \land (B \subseteq D))$,which by De Morgan's Law is $(A 
ot\subseteq B) \lor (B 
ot\subseteq D)$.Thus,the contrapositive is: "If $A 
ot\subseteq C,$ then $A 
ot\subseteq B$ or $B 
ot\subseteq D$."

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

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