Provide a Venn diagram of a counter example of the converse of if A ⊆ B, then A ∪ C ⊆ B ∪ C? Provide a Venn diagram of a counter example of the converse of 

$$A \subseteq B\rightarrow ((A \cup C) \subseteq (B \cup C))$$
First of all, we need to clearly state the converse of

$$ (A ⊆ B) \rightarrow [(A ∪ C) ⊆ (B ∪ C)].\tag 1$$  

The converse of $(1)$ is as follows: 

$$[(A ∪ C) ⊆ (B ∪ C)]\rightarrow (A\subseteq B)\tag{2}$$

One counterexample to the converse (2):  $$\text{Suppose } \;A = \{1\}, \;B=\{2\}, \;C=\{1,2\}$$ 

Then, it is true that $((A ∪ C) = C) ⊆ ((B ∪ C) = C)$ but $A\not \subseteq B$ because $\{1\} \not \subseteq \{2\}$
Consider  when B is a proper subset of A is a proper subset of C.