Let A, B and C be sets such that $\mathrm{\varphi }\ne \mathrm{A}\cap \mathrm{B}\subseteq \mathrm{C}$.Then which of the following statements is not true?

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

Here, $\mathrm{A}\cap \mathrm{B}\subseteq \mathrm{C} \text{and }\mathrm{A}\cap \mathrm{B}\ne \mathrm{\varphi }$

Now, from the Venn diagram, it is clear that

$\mathrm{B}\cap \mathrm{C}\ne \mathrm{\varphi }$ is true,

Also,$(\mathrm{C}\cup \mathrm{A})\cap (\mathrm{C}\cup \mathrm{B})=\mathrm{C}\cup (\mathrm{A}\cap \mathrm{B})=\mathrm{C}$ is true

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

From the Venn diagram, it is clear that

If $\mathrm{A}-\mathrm{B}\subseteq \mathrm{C},$ and $\mathrm{A}\subseteq \mathrm{C}$

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

from the Venn diagram, it is clear that

$\mathrm{A}\cap \mathrm{B}\ne \mathrm{\varphi },\mathrm{A}\cap \mathrm{B}\subseteq \mathrm{C}$ and $\mathrm{A}-\mathrm{C}=\mathrm{\varphi }\subseteq \mathrm{B}$ but $\mathrm{A}⊈\mathrm{B}$