JEE Main 2019 — Sets And Relations Question with Solution

According to the question, we have the following Venn diagram.

Here, $A\cap B\subseteq C$ and $A\cap B\ne \varphi$


Now, from the Venn diagram, it is clear that $B\cap C\ne \varphi$, is true

Also, $(C\cup A)\cap (C\cup B)=C\cup (A\cap B)=C$ is true.

If $(A-B)\subseteq C$, for this statement the Venn diagram is


From the Venn diagram, it is clear that if $A-B\subseteq C$, then $A\subseteq C$.

Now, if $(A-C)\subseteq B$, for this statement the Venn diagram.


From the Venn diagram, it is clear that

$A\cap B\ne \varphi ,A\cap B\subseteq C$ and $A-C=\varphi \subseteq B$ but $A\subseteq B$