Question

Draw the Venn diagrams for each of these combinations of sets A, B, C, and D.

a) \(\left( {A \cap B} \right) \cup \left( {C \cap D} \right)\)

b) \(\mathop A\limits^\_ \cup \mathop B\limits^\_ \cup \mathop C\limits^\_ \cup \mathop D\limits^\_ \)

c) \(A - \left( {B \cap C \cap D} \right)\)

Short answer

Thus, our Venn diagrams are,

a)

b)

c)

Step-by-step solution

Given

Given in the question A, B, C, and D is a set. we need to draw its Venn diagram.

solution for part (a)

Here we first need two draw Venn diagrams, \(A \cap B\).

Here we draw the Venn Diagram\(C \cap D\).

Here we finally draw the Venn diagram\(\left( {A \cap B} \right) \cup \left( {C \cap D} \right)\).

solution for part (b)

Here we need to first draw the Venn diagram\(\mathop A\limits^\_ \cup \mathop B\limits^\_ \).

Now we need to draw the Venn diagram\(\mathop C\limits^\_ \cup \mathop D\limits^\_ \).

Now we finally draw the Venn diagram\(\mathop A\limits^\_ \cup \mathop B\limits^\_ \cup \mathop C\limits^\_ \cup \mathop D\limits^\_ \).

solution for part (c)

Now here we draw the Venn diagram, \(B \cap C \cap D\).

Now here we draw the Venn diagram of \(A - \left( {B \cap C \cap D} \right)\).