Let A,B and C be sets such that A B C.

Question

Let $A,B$ and $C$ be sets such that $\emptyset
eq A\cap B\subseteq C$. Then which of the following statements is not true?

Accepted Answer

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

Here, $A \cap B \subseteq C$ and $A \cap B 
eq \phi$

Now, from the Venn diagram, it is clear that $B \cap C 
eq \phi$, 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

$A \cap B 
eq \phi, A \cap B \subseteq C$ and $A-C=\phi \subseteq B$ but $A \subseteq B$

Solutions · 1