JEE Main 2019 (Online) 12th April Evening ShiftQuestion 1
Let $A$, $B$ and $C$ be sets such that $\phi\neq A\cap B\subseteq C$. Then which of the following statements is not true?
Sets, Relations and Function
Solution
$A\cap B\subseteq B\cap C$ gives $B\cap C\neq\phi$; $(C\cup A)\cap(C\cup B)=C\cup(A\cap B)=C$; $A=(A-B)\cup(A\cap B)\subseteq C$. For the last one, $A=\{1,2\},B=\{1\},C=\{1,2\}$ gives $A-C=\phi\subseteq B$ but $A\not\subseteq B$. False: if $A-C\subseteq B$ then $A\subseteq B$.