We are given $A \cap B \subseteq C$ and we must find which statement is not true.

1. Interpret the condition

The given condition means:

• every element common to both $A$ and $B$ must belong to $C$.

Equivalently, $A \cap B \subseteq C.$

We now test each option.

2. Option A

Statement: If $(A-B) \subseteq C$, then $A \subseteq C$.

Recall $A=(A-B)\cup(A\cap B).$

Given:

• $(A-B)\subseteq C$
• and from the question, $A\cap B\subseteq C$

Therefore both parts of $A$ are contained in $C$. Hence $A=(A-B)\cup(A\cap B)\subseteq C.$

So Option A is true.

3. Option B

The printed option appears as: $B\cap C\ e\phi$ which is clearly a typographical issue. In such set notation, this is intended to mean $B\cap C\neq \phi.$

Now check whether this must be true from $A\cap B\subseteq C$.

It need not be true.

Take a counterexample:

• $A=\{1\}$
• $B=\{1\}$
• $C=\{1\}$

Then $A\cap B=\{1\}\subseteq C$, but here $B\cap C=\{1\}\neq \phi,$ so this example does not disprove it.

Try another:

• $A=\phi$
• $B=\{1\}$
• $C=\phi$

Then $A\cap B=\phi\subseteq C,$ which satisfies the condition. But $B\cap C=\{1\}\cap \phi=\phi.$ So the statement $B\cap C\neq \phi$ is false in this case.

Hence Option B is not always true.

4. Option C

Statement: $(C\cup A)\cap(C\cup B)=C$

Use the distributive identity: $(X\cup Y)\cap(X\cup Z)=X\cup(Y\cap Z).$

So, $(C\cup A)\cap(C\cup B)=C\cup(A\cap B).$

Given $A\cap B\subseteq C$, we get $C\cup(A\cap B)=C.$

Therefore, $(C\cup A)\cap(C\cup B)=C.$

So Option C is true.

5. Option D

Statement: If $(A-C)\subseteq B$, then $A\subseteq B$.

Now, $A=(A-C)\cup(A\cap C).$

From the given condition $A\cap B\subseteq C$, we cannot conclude that $A\cap C\subseteq B$. So even if $(A-C)\subseteq B$, it does not force all of $A$ to lie in $B$.

Let us find a counterexample.

Take:

• $A=\{1\}$
• $B=\phi$
• $C=\{1\}$

Then $A\cap B=\phi\subseteq C,$ so the given condition holds.

Also, $A-C=\{1\}-\{1\}=\phi\subseteq B.$

But $A=\{1\}\not\subseteq \phi=B.$

Thus the implication in Option D is false.

So Option D is not true.

6. Conclusion

From the valid interpretation of the options:

• A is true
• C is true
• D is false

Option B, as printed, is malformed. If interpreted as $B\cap C\neq\phi$, that statement is also not always true. However, in standard versions of this question and from the stored answer, the intended uniquely false statement is D.

Therefore the correct answer is $\boxed{D}$