Sets, Relations and Function: Let A,B,C and D be four non-empty sets. The contrapositive statement… | JEE Main 2020

JEE Main 2020 (Online) 7th January Evening ShiftQuestion 1

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 :

Sets, Relations and Function

If $A\not\subseteq C$, then $A\subseteq B$ and $B\subseteq D$If $A\subseteq C$, then $B\subset A$ and $D\subset B$If $A\not\subseteq C$, then $A\not\subseteq B$ and $B\subseteq D$If $A\not\subseteq C$, then $A\not\subseteq B$ or $B\not\subseteq D$✓ Correct answer

Solution

Contrapositive of $(X\wedge Y)\Rightarrow Z$ is $\sim Z\Rightarrow\sim(X\wedge Y)=\sim Z\Rightarrow(\sim X\vee\sim Y)$: if $A\not\subseteq C$, then $A\not\subseteq B$ or $B\not\subseteq D$.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2020 (Online) 7th January Evening Shift)

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