3. Let A, B, C, and D be subsets of some universal set U. Consider the two propositions:
(I) If $A \subseteq B$ and $C \subseteq D$ and B and D are disjoint, then A and C are disjoint.
(II) If $A \subseteq B$ and $C \subseteq D$ and A and C are disjoint, then B and D are disjoint.
a. Use Venn diagrams to make a conjecture about which of the two statements
is true, and which is false.
b. Write a proof of the true proposition. (Hint: Try a proof by contradiction!)
c. Provide a specific (counter)example of sets that shows that the false
statement is false.
