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  • Let A,B,C and D be four non-empty sets. The contrapositive statement of '' If  and <img alt="B\subseteq D," src="https://learn.careers360.com

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 :
Option: 1 If A\subseteq C, then B\subset A or D\subset B  
Option: 2 If A\nsubseteq C, then A\subseteq B and B\subseteq D
Option: 3 If A\nsubseteq C,, then A\nsubseteq B and B\subseteq D
Option: 4 If A\nsubseteq C,, then A\nsubseteq B and B\nsubseteq D

Answers (1)

best_answer

 

 

Converse, Inverse, and Contrapositive -

Given an if-then statement "if p , then q ," we can create three related statements:

A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.  For instance, “If you are born in some country, then you are a citizen of that country” 

"you are born in some country" is the hypothesis.

"you are a citizen of that country" is the conclusion.

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

The Contrapositive of  “If you are born in some country, then you are a citizen of that country” 

is  “If you are not a citizen of that country, then you are not born in some country.”

\begin{array}{|c|c|c|}\hline \text { \;\;Statement\;\; } & \mathrm{\;\;\;}{\text { If } p, \text { then } q} \mathrm{\;\;\;}& \mathrm{\;\;\;}p\rightarrow q \mathrm{\;\;\;}\\ \hline \text { Converse } & \mathrm{\;\;\;}{\text { If } q, \text { then } p} \mathrm{\;\;\;}&\mathrm{\;\;\;}q\rightarrow p \mathrm{\;\;\;} \\ \hline \text { Inverse } & \mathrm{\;\;\;}{\text { If not } p, \text { then not } q} \mathrm{\;\;\;}& \mathrm{\;\;\;}(\sim p) \rightarrow(\sim q) \mathrm{\;\;\;} \\ \hline \text { Contrapositive } & \mathrm{\;\;\;}{\text { If not } q, \text { then not } p} \mathrm{\;\;\;}& \mathrm{\;\;\;}(\sim q) \rightarrow(\sim p) \mathrm{\;\;\;}\\ \hline\end{array}

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\\\text { Let } P=A \subseteq B, Q=B \subseteq D, R=A \subseteq C\\\text{contrapositive of }(P\wedge Q)\rightarrow R\;\text{ is}\\\sim R \rightarrow \sim (P\wedge Q)\\\text{i.e.}\;\;\;\sim R\rightarrow (\sim P\vee \sim Q)

Hence, \text { If } A \nsubseteq C, \text { then } A \nsubseteq B \text { or } B \not \neq D

Correct Option (4)

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Ritika Jonwal

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