Question

each venn diagram has sets a, b, and the universal set u. (a) shade (a∪b). (b) shade a∩b.

Explanation:

Step1: Define $(A \cup B)'$

$(A \cup B)'$ is the complement of the union of $A$ and $B$, meaning all elements in the universal set $U$ that are not in $A$ or $B$.

Step2: Shade region for $(A \cup B)'$

In the first Venn diagram, shade the area inside rectangle $U$ but outside both circles $A$ and $B$.

Step3: Define $A' \cap B'$

By De Morgan's Law, $A' \cap B' = (A \cup B)'$, so it represents elements not in $A$ and not in $B$, identical to the region in Step 2.

Step4: Shade region for $A' \cap B'$

In the second Venn diagram, shade the area inside rectangle $U$ but outside both circles $A$ and $B$.

Answer:

(a) Shaded area: The portion of the universal set $U$ that is outside both circle $A$ and circle $B$.
(b) Shaded area: The portion of the universal set $U$ that is outside both circle $A$ and circle $B$.

(Visual description: For both diagrams, shade the white space inside the outer rectangle that is not covered by either of the two overlapping circles.)